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
$begingroup$
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).
graph-theory recreational-mathematics coloring
$endgroup$
|
show 2 more comments
$begingroup$
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).
graph-theory recreational-mathematics coloring
$endgroup$
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
|
show 2 more comments
$begingroup$
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).
graph-theory recreational-mathematics coloring
$endgroup$
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
graph-theory recreational-mathematics coloring
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
|
show 2 more comments
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
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
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:
Adjacencies between the states may be easier to see here.
$endgroup$
$begingroup$
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
|
show 6 more comments
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
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
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:
Adjacencies between the states may be easier to see here.
$endgroup$
$begingroup$
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
|
show 6 more comments
$begingroup$
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:
Adjacencies between the states may be easier to see here.
$endgroup$
$begingroup$
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
|
show 6 more comments
$begingroup$
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:
Adjacencies between the states may be easier to see here.
$endgroup$
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:
Adjacencies between the states may be easier to see here.
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
|
show 6 more comments
$begingroup$
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
|
show 6 more comments
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.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
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