How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the colour of Green Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Did the Appel/Haken graph colouring (four colour map) proof really not contribute to understanding?How many four-vertex graphs are there up to isomorphism;$Z_n backslash 0$ splits into octetsHow many different cubes can be obtained if four colours are used?Coloring the 6 vertices of a regular hexagon with a limited use per colorKempe's proof of the four colour theoremAlgorithm to solve this grid puzzle?Explain this proof of the 5-color theoremFinding a maximum connected planar graph to prove the four colour theoremGraph colouring problem

Communication vs. Technical skills ,which is more relevant for today's QA engineer positions?

Fishing simulator

Why is there no army of Iron-Mans in the MCU?

Can smartphones with the same camera sensor have different image quality?

How to dynamically generate the hash value of a file while it gets downloaded from any website?

Is it possible to ask for a hotel room without minibar/extra services?

Complexity of many constant time steps with occasional logarithmic steps

Losing the Initialization Vector in Cipher Block Chaining

Why use gamma over alpha radiation?

How to pour concrete for curved walkway to prevent cracking?

I'm having difficulty getting my players to do stuff in a sandbox campaign

Need a suitable toxic chemical for a murder plot in my novel

How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time

How do I automatically answer y in bash script?

How do you clear the ApexPages.getMessages() collection in a test?

Why does this iterative way of solving of equation work?

Is there folklore associating late breastfeeding with low intelligence and/or gullibility?

Replacing HDD with SSD; what about non-APFS/APFS?

Are my PIs rude or am I just being too sensitive?

How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the colour of Green

Make it rain characters

Using "nakedly" instead of "with nothing on"

Classification of bundles, Postnikov towers, obstruction theory, local coefficients

What is the largest species of polychaete?



How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the colour of Green



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Did the Appel/Haken graph colouring (four colour map) proof really not contribute to understanding?How many four-vertex graphs are there up to isomorphism;$Z_n backslash 0$ splits into octetsHow many different cubes can be obtained if four colours are used?Coloring the 6 vertices of a regular hexagon with a limited use per colorKempe's proof of the four colour theoremAlgorithm to solve this grid puzzle?Explain this proof of the 5-color theoremFinding a maximum connected planar graph to prove the four colour theoremGraph colouring problem










19












$begingroup$


I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other colours as much as we want. Please note that I want to follow the Four Color Theorem rules.



Motivation:
I am studying graph theory and I want to know if there is a way that we could limit the use of the fourth colour as much as possible. This is not a homework problem.



My attempt:
I have tried many variations and can limit it to 6 and it seems like the
minimum possible but there are many possibilities to try ($4^50$). Therefore I was wondering if there is a simpler method? Thank you in advance.



Clarification:
I am interested in only the mainland of USA. For states like Michigan that are split, I used the same colour for both parts (since they were not connected directly).










share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
    $endgroup$
    – Will Jagy
    19 hours ago






  • 1




    $begingroup$
    blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
    $endgroup$
    – Will Jagy
    19 hours ago










  • $begingroup$
    thank you for your suggestion, I made a few clarifications.
    $endgroup$
    – Bor Kari
    18 hours ago










  • $begingroup$
    @WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
    $endgroup$
    – Marc van Leeuwen
    5 hours ago






  • 1




    $begingroup$
    There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
    $endgroup$
    – Derek Elkins
    2 hours ago















19












$begingroup$


I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other colours as much as we want. Please note that I want to follow the Four Color Theorem rules.



Motivation:
I am studying graph theory and I want to know if there is a way that we could limit the use of the fourth colour as much as possible. This is not a homework problem.



My attempt:
I have tried many variations and can limit it to 6 and it seems like the
minimum possible but there are many possibilities to try ($4^50$). Therefore I was wondering if there is a simpler method? Thank you in advance.



Clarification:
I am interested in only the mainland of USA. For states like Michigan that are split, I used the same colour for both parts (since they were not connected directly).










share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
    $endgroup$
    – Will Jagy
    19 hours ago






  • 1




    $begingroup$
    blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
    $endgroup$
    – Will Jagy
    19 hours ago










  • $begingroup$
    thank you for your suggestion, I made a few clarifications.
    $endgroup$
    – Bor Kari
    18 hours ago










  • $begingroup$
    @WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
    $endgroup$
    – Marc van Leeuwen
    5 hours ago






  • 1




    $begingroup$
    There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
    $endgroup$
    – Derek Elkins
    2 hours ago













19












19








19


2



$begingroup$


I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other colours as much as we want. Please note that I want to follow the Four Color Theorem rules.



Motivation:
I am studying graph theory and I want to know if there is a way that we could limit the use of the fourth colour as much as possible. This is not a homework problem.



My attempt:
I have tried many variations and can limit it to 6 and it seems like the
minimum possible but there are many possibilities to try ($4^50$). Therefore I was wondering if there is a simpler method? Thank you in advance.



Clarification:
I am interested in only the mainland of USA. For states like Michigan that are split, I used the same colour for both parts (since they were not connected directly).










share|cite|improve this question











$endgroup$




I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other colours as much as we want. Please note that I want to follow the Four Color Theorem rules.



Motivation:
I am studying graph theory and I want to know if there is a way that we could limit the use of the fourth colour as much as possible. This is not a homework problem.



My attempt:
I have tried many variations and can limit it to 6 and it seems like the
minimum possible but there are many possibilities to try ($4^50$). Therefore I was wondering if there is a simpler method? Thank you in advance.



Clarification:
I am interested in only the mainland of USA. For states like Michigan that are split, I used the same colour for both parts (since they were not connected directly).







graph-theory recreational-mathematics coloring






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 hours ago







Bor Kari

















asked 19 hours ago









Bor KariBor Kari

44910




44910







  • 1




    $begingroup$
    you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
    $endgroup$
    – Will Jagy
    19 hours ago






  • 1




    $begingroup$
    blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
    $endgroup$
    – Will Jagy
    19 hours ago










  • $begingroup$
    thank you for your suggestion, I made a few clarifications.
    $endgroup$
    – Bor Kari
    18 hours ago










  • $begingroup$
    @WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
    $endgroup$
    – Marc van Leeuwen
    5 hours ago






  • 1




    $begingroup$
    There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
    $endgroup$
    – Derek Elkins
    2 hours ago












  • 1




    $begingroup$
    you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
    $endgroup$
    – Will Jagy
    19 hours ago






  • 1




    $begingroup$
    blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
    $endgroup$
    – Will Jagy
    19 hours ago










  • $begingroup$
    thank you for your suggestion, I made a few clarifications.
    $endgroup$
    – Bor Kari
    18 hours ago










  • $begingroup$
    @WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
    $endgroup$
    – Marc van Leeuwen
    5 hours ago






  • 1




    $begingroup$
    There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
    $endgroup$
    – Derek Elkins
    2 hours ago







1




1




$begingroup$
you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
$endgroup$
– Will Jagy
19 hours ago




$begingroup$
you would need to agree on a favorite version of the graph. In the actual US, there are islands, states split into disconnected regions, other things forbidden
$endgroup$
– Will Jagy
19 hours ago




1




1




$begingroup$
blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
$endgroup$
– Will Jagy
19 hours ago




$begingroup$
blog.computationalcomplexity.org/2006/05/… They correctly point out that three colors cannot work, as Nevada has an odd number of neighbors
$endgroup$
– Will Jagy
19 hours ago












$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
18 hours ago




$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
18 hours ago












$begingroup$
@WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
$endgroup$
– Marc van Leeuwen
5 hours ago




$begingroup$
@WillJagy Maine has an odd number of neighbours too, but that's not much of a problem.
$endgroup$
– Marc van Leeuwen
5 hours ago




1




1




$begingroup$
There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
$endgroup$
– Derek Elkins
2 hours ago




$begingroup$
There are not infinite possibilities. There is only $4^50$ ways of assigning colors to all the states even if we consider no other constraints or symmetries.
$endgroup$
– Derek Elkins
2 hours ago










1 Answer
1






active

oldest

votes


















22












$begingroup$

The minimum is two states that use the fourth color. Nevada and its five neighbors cannot be colored with only three colors, and similarly West Virginia and its five neighbors cannot be colored with only three colors. In both cases, once you color the center state one color (say, red), you can't use it again on its neighbors: without using green, they'd have to alternate yellow-blue-yellow-blue, but because the number of neighbors is odd, you'd get stuck at the end.



(In the comments, David K points out that Kentucky is a third state with the same problem: it has seven neighbors. But this doesn't force us to use a third green state, because Kentucky and West Virginia share a border and some common neighbors.)



Using only two green states is possible. If we color Arizona (dealing with the Nevada situation) and Ohio (dealing with West Virginia and Kentucky) both green, then the remainder of the map can be completed using only blue, red, and yellow:



enter image description here



Adjacencies between the states may be easier to see here.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
    $endgroup$
    – Will Jagy
    18 hours ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    17 hours ago






  • 3




    $begingroup$
    @antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
    $endgroup$
    – Misha Lavrov
    16 hours ago







  • 1




    $begingroup$
    @WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
    $endgroup$
    – hobbs
    15 hours ago






  • 2




    $begingroup$
    Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
    $endgroup$
    – David K
    9 hours ago












Your Answer








StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3186983%2fhow-to-colour-the-us-map-with-yellow-green-red-and-blue-to-minimize-the-number%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









22












$begingroup$

The minimum is two states that use the fourth color. Nevada and its five neighbors cannot be colored with only three colors, and similarly West Virginia and its five neighbors cannot be colored with only three colors. In both cases, once you color the center state one color (say, red), you can't use it again on its neighbors: without using green, they'd have to alternate yellow-blue-yellow-blue, but because the number of neighbors is odd, you'd get stuck at the end.



(In the comments, David K points out that Kentucky is a third state with the same problem: it has seven neighbors. But this doesn't force us to use a third green state, because Kentucky and West Virginia share a border and some common neighbors.)



Using only two green states is possible. If we color Arizona (dealing with the Nevada situation) and Ohio (dealing with West Virginia and Kentucky) both green, then the remainder of the map can be completed using only blue, red, and yellow:



enter image description here



Adjacencies between the states may be easier to see here.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
    $endgroup$
    – Will Jagy
    18 hours ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    17 hours ago






  • 3




    $begingroup$
    @antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
    $endgroup$
    – Misha Lavrov
    16 hours ago







  • 1




    $begingroup$
    @WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
    $endgroup$
    – hobbs
    15 hours ago






  • 2




    $begingroup$
    Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
    $endgroup$
    – David K
    9 hours ago
















22












$begingroup$

The minimum is two states that use the fourth color. Nevada and its five neighbors cannot be colored with only three colors, and similarly West Virginia and its five neighbors cannot be colored with only three colors. In both cases, once you color the center state one color (say, red), you can't use it again on its neighbors: without using green, they'd have to alternate yellow-blue-yellow-blue, but because the number of neighbors is odd, you'd get stuck at the end.



(In the comments, David K points out that Kentucky is a third state with the same problem: it has seven neighbors. But this doesn't force us to use a third green state, because Kentucky and West Virginia share a border and some common neighbors.)



Using only two green states is possible. If we color Arizona (dealing with the Nevada situation) and Ohio (dealing with West Virginia and Kentucky) both green, then the remainder of the map can be completed using only blue, red, and yellow:



enter image description here



Adjacencies between the states may be easier to see here.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
    $endgroup$
    – Will Jagy
    18 hours ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    17 hours ago






  • 3




    $begingroup$
    @antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
    $endgroup$
    – Misha Lavrov
    16 hours ago







  • 1




    $begingroup$
    @WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
    $endgroup$
    – hobbs
    15 hours ago






  • 2




    $begingroup$
    Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
    $endgroup$
    – David K
    9 hours ago














22












22








22





$begingroup$

The minimum is two states that use the fourth color. Nevada and its five neighbors cannot be colored with only three colors, and similarly West Virginia and its five neighbors cannot be colored with only three colors. In both cases, once you color the center state one color (say, red), you can't use it again on its neighbors: without using green, they'd have to alternate yellow-blue-yellow-blue, but because the number of neighbors is odd, you'd get stuck at the end.



(In the comments, David K points out that Kentucky is a third state with the same problem: it has seven neighbors. But this doesn't force us to use a third green state, because Kentucky and West Virginia share a border and some common neighbors.)



Using only two green states is possible. If we color Arizona (dealing with the Nevada situation) and Ohio (dealing with West Virginia and Kentucky) both green, then the remainder of the map can be completed using only blue, red, and yellow:



enter image description here



Adjacencies between the states may be easier to see here.






share|cite|improve this answer











$endgroup$



The minimum is two states that use the fourth color. Nevada and its five neighbors cannot be colored with only three colors, and similarly West Virginia and its five neighbors cannot be colored with only three colors. In both cases, once you color the center state one color (say, red), you can't use it again on its neighbors: without using green, they'd have to alternate yellow-blue-yellow-blue, but because the number of neighbors is odd, you'd get stuck at the end.



(In the comments, David K points out that Kentucky is a third state with the same problem: it has seven neighbors. But this doesn't force us to use a third green state, because Kentucky and West Virginia share a border and some common neighbors.)



Using only two green states is possible. If we color Arizona (dealing with the Nevada situation) and Ohio (dealing with West Virginia and Kentucky) both green, then the remainder of the map can be completed using only blue, red, and yellow:



enter image description here



Adjacencies between the states may be easier to see here.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 8 hours ago

























answered 18 hours ago









Misha LavrovMisha Lavrov

49.5k758109




49.5k758109











  • $begingroup$
    I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
    $endgroup$
    – Will Jagy
    18 hours ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    17 hours ago






  • 3




    $begingroup$
    @antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
    $endgroup$
    – Misha Lavrov
    16 hours ago







  • 1




    $begingroup$
    @WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
    $endgroup$
    – hobbs
    15 hours ago






  • 2




    $begingroup$
    Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
    $endgroup$
    – David K
    9 hours ago

















  • $begingroup$
    I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
    $endgroup$
    – Will Jagy
    18 hours ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    17 hours ago






  • 3




    $begingroup$
    @antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
    $endgroup$
    – Misha Lavrov
    16 hours ago







  • 1




    $begingroup$
    @WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
    $endgroup$
    – hobbs
    15 hours ago






  • 2




    $begingroup$
    Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
    $endgroup$
    – David K
    9 hours ago
















$begingroup$
I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
$endgroup$
– Will Jagy
18 hours ago




$begingroup$
I need a better atlas. I'm looking at the Philadelphia area, I cannot tell what happens among Pennsylvania, New Jersey, Delaware, Maryland.
$endgroup$
– Will Jagy
18 hours ago




2




2




$begingroup$
just curious -- did you write code to do this, or did you do this by hand?
$endgroup$
– antkam
17 hours ago




$begingroup$
just curious -- did you write code to do this, or did you do this by hand?
$endgroup$
– antkam
17 hours ago




3




3




$begingroup$
@antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
$endgroup$
– Misha Lavrov
16 hours ago





$begingroup$
@antkam By hand. I found two subgraphs where a fourth color is forced, and chose a state from each of them to color green that seemed to be a good choice. Then I just tried to color the rest with three colors - and for that, once you color the first two states, most of the rest of the map is forced, except for a few states like Maine.
$endgroup$
– Misha Lavrov
16 hours ago





1




1




$begingroup$
@WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
$endgroup$
– hobbs
15 hours ago




$begingroup$
@WillJagy NJ and MD don't touch because DE interposes. All the other edges exist.
$endgroup$
– hobbs
15 hours ago




2




2




$begingroup$
Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
$endgroup$
– David K
9 hours ago





$begingroup$
Kentucky has seven neighbors, but coloring Ohio green fixes that as well as WV. I also notice that you managed to use four colors for UT, CO, AZ, and NM, which makes the map a little clearer but I think is not strictly required by the usual rules, that is, under the usual rules (as far as I know) you could make AZ yellow and CA green.
$endgroup$
– David K
9 hours ago


















draft saved

draft discarded
















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3186983%2fhow-to-colour-the-us-map-with-yellow-green-red-and-blue-to-minimize-the-number%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-coloring, graph-theory, recreational-mathematics

Popular posts from this blog

Mobil Contents History Mobil brands Former Mobil brands Lukoil transaction Mobil UK Mobil Australia Mobil New Zealand Mobil Greece Mobil in Japan Mobil in Canada Mobil Egypt See also References External links Navigation menuwww.mobil.com"Mobil Corporation"the original"Our Houston campus""Business & Finance: Socony-Vacuum Corp.""Popular Mechanics""Lubrite Technologies""Exxon Mobil campus 'clearly happening'""Toledo Blade - Google News Archive Search""The Lion and the Moose - How 2 Executives Pulled off the Biggest Merger Ever""ExxonMobil Press Release""Lubricants""Archived copy"the original"Mobil 1™ and Mobil Super™ motor oil and synthetic motor oil - Mobil™ Motor Oils""Mobil Delvac""Mobil Industrial website""The State of Competition in Gasoline Marketing: The Effects of Refiner Operations at Retail""Mobil Travel Guide to become Forbes Travel Guide""Hotel Rankings: Forbes Merges with Mobil"the original"Jamieson oil industry history""Mobil news""Caltex pumps for control""Watchdog blocks Caltex bid""Exxon Mobil sells service station network""Mobil Oil New Zealand Limited is New Zealand's oldest oil company, with predecessor companies having first established a presence in the country in 1896""ExxonMobil subsidiaries have a business history in New Zealand stretching back more than 120 years. We are involved in petroleum refining and distribution and the marketing of fuels, lubricants and chemical products""Archived copy"the original"Exxon Mobil to Sell Its Japanese Arm for $3.9 Billion""Gas station merger will end Esso and Mobil's long run in Japan""Esso moves to affiliate itself with PC Optimum, no longer Aeroplan, in loyalty point switch""Mobil brand of gas stations to launch in Canada after deal for 213 Loblaws-owned locations""Mobil Nears Completion of Rebranding 200 Loblaw Gas Stations""Learn about ExxonMobil's operations in Egypt""Petrol and Diesel Service Stations in Egypt - Mobil"Official websiteExxon Mobil corporate websiteMobil Industrial official websiteeeeeeeeDA04275022275790-40000 0001 0860 5061n82045453134887257134887257

Frič See also Navigation menuinternal link

My Life (Mary J. Blige album) Contents Background Critical reception Accolades Commercial performance Track listing Personnel Charts Certifications See also References External links Navigation menu"1. Mary J Blige, My Life - The 50 Best R&B albums of the '90s""American album certifications – Mary J. Blige – My Life""Mary J. Blige's My Life LP (1994) revisited with co-producer Chucky Thompson | Return To The Classics"the original"Key Tracks: Mary J. Blige's My Life""My Life – Mary J. Blige""Worth The Wait""My Life""Forget '411,' Mary J., Better Call 911""Spins"My Life AccoladesThe 500 Greatest Albums of All TimeTime's All-TIME 100 Albums"Top RPM Albums: Issue chartid""Dutchcharts.nl – Mary J. Blige – My Life""Mary J. Blige | Artist | Official Charts""Mary J. Blige Chart History (Billboard 200)""Mary J. Blige Chart History (Top R&B/Hip-Hop Albums)""Canadian album certifications – Mary J Blige – My Life""British album certifications – Mary J Blige – My Life""American album certifications – Mary J Blige – My Life"My LifeMy Life accoladesee