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

First use of “packing” as in carrying a gun

Am I ethically obligated to go into work on an off day if the reason is sudden?

Semisimplicity of the category of coherent sheaves?

How many people can fit inside Mordenkainen's Magnificent Mansion?

How to copy the contents of all files with a certain name into a new file?

How can I protect witches in combat who wear limited clothing?

Was credit for the black hole image misattributed?

How to delete random line from file using Unix command?

The variadic template constructor of my class cannot modify my class members, why is that so?

How long does the line of fire that you can create as an action using the Investiture of Flame spell last?

Difference between "generating set" and free product?

Multiple regression results help

does high air pressure throw off wheel balance?

Cooking pasta in a water boiler

What aspect of planet Earth must be changed to prevent the industrial revolution?

Can a 1st-level character have an ability score above 18?

University's motivation for having tenure-track positions

How does ice melt when immersed in water?

Why does the Event Horizon Telescope (EHT) not include telescopes from Africa, Asia or Australia?

Single author papers against my advisor's will?

What is special about square numbers here?

Can the DM override racial traits?

Do working physicists consider Newtonian mechanics to be "falsified"?

Why did all the guest students take carriages to the Yule Ball?



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



The 2019 Stack Overflow Developer Survey Results Are In
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?Counterexamples to proofs of correct statementsHow many Latin Squares are there with the following restrictions?$Z_n backslash {0}$ splits into octetsKempe'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 theoremThe $n$-astrolabacus sequence.Strategies in Memory game












7












$begingroup$


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 infinite possibilities to try so 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
    2 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
    2 hours ago










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










  • $begingroup$
    I've edited your title to make it more specific and informative. Please check if it is correct.
    $endgroup$
    – YuiTo Cheng
    30 mins ago
















7












$begingroup$


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 infinite possibilities to try so 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
    2 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
    2 hours ago










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










  • $begingroup$
    I've edited your title to make it more specific and informative. Please check if it is correct.
    $endgroup$
    – YuiTo Cheng
    30 mins ago














7












7








7


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 infinite possibilities to try so 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 infinite possibilities to try so 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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 30 mins ago









YuiTo Cheng

2,40641037




2,40641037










asked 2 hours ago









Bor KariBor Kari

3749




3749








  • 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
    2 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
    2 hours ago










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










  • $begingroup$
    I've edited your title to make it more specific and informative. Please check if it is correct.
    $endgroup$
    – YuiTo Cheng
    30 mins 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
    2 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
    2 hours ago










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










  • $begingroup$
    I've edited your title to make it more specific and informative. Please check if it is correct.
    $endgroup$
    – YuiTo Cheng
    30 mins 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
2 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
2 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
2 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
2 hours ago












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




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












$begingroup$
I've edited your title to make it more specific and informative. Please check if it is correct.
$endgroup$
– YuiTo Cheng
30 mins ago




$begingroup$
I've edited your title to make it more specific and informative. Please check if it is correct.
$endgroup$
– YuiTo Cheng
30 mins ago










1 Answer
1






active

oldest

votes


















5












$begingroup$

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.



But if we color Arizona and Ohio a color we use nowhere else, then the remainder of the map can be completed using only three colors:



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
    1 hour ago










  • $begingroup$
    @WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    1 hour ago






  • 2




    $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    1 hour 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
    1 min 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









5












$begingroup$

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.



But if we color Arizona and Ohio a color we use nowhere else, then the remainder of the map can be completed using only three colors:



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
    1 hour ago










  • $begingroup$
    @WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    1 hour ago






  • 2




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


















5












$begingroup$

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.



But if we color Arizona and Ohio a color we use nowhere else, then the remainder of the map can be completed using only three colors:



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
    1 hour ago










  • $begingroup$
    @WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    1 hour ago






  • 2




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
















5












5








5





$begingroup$

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.



But if we color Arizona and Ohio a color we use nowhere else, then the remainder of the map can be completed using only three colors:



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.



But if we color Arizona and Ohio a color we use nowhere else, then the remainder of the map can be completed using only three colors:



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 1 hour ago

























answered 2 hours ago









Misha LavrovMisha Lavrov

49.3k757108




49.3k757108












  • $begingroup$
    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
    1 hour ago










  • $begingroup$
    @WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    1 hour ago






  • 2




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










  • $begingroup$
    @WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    1 hour ago






  • 2




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












$begingroup$
@WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
$endgroup$
– Misha Lavrov
1 hour ago




$begingroup$
@WillJagy The reference I actually used to color the US was this picture of the US graph, which solves this problem.
$endgroup$
– Misha Lavrov
1 hour ago












$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
1 hour ago




$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
1 hour ago




2




2




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




$begingroup$
just curious -- did you write code to do this, or did you do this by hand?
$endgroup$
– antkam
1 hour 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
1 min 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
1 min 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







Popular posts from this blog

“%fieldName is a required field.”, in Magento2 REST API Call for GET Method Type The Next...

How to change City field to a dropdown in Checkout step Magento 2Magento 2 : How to change UI field(s)...

變成蝙蝠會怎樣? 參考資料 外部連結 导航菜单Thomas Nagel, "What is it like to be a...