Four Colour Theorem The 2019 Stack Overflow Developer Survey Results Are In ...

Wall plug outlet change

Didn't get enough time to take a Coding Test - what to do now?

does high air pressure throw off wheel balance?

How to pronounce 1ターン?

How did passengers keep warm on sail ships?

Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?

University's motivation for having tenure-track positions

Did the new image of black hole confirm the general theory of relativity?

Can withdrawing asylum be illegal?

Single author papers against my advisor's will?

Does Parliament need to approve the new Brexit delay to 31 October 2019?

Why can't devices on different VLANs, but on the same subnet, communicate?

Mortgage adviser recommends a longer term than necessary combined with overpayments

Cooking pasta in a water boiler

Is above average number of years spent on PhD considered a red flag in future academia or industry positions?

What information about me do stores get via my credit card?

What do you call a plan that's an alternative plan in case your initial plan fails?

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

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

Why does this iterative way of solving of equation work?

Slither Like a Snake

Python - Fishing Simulator

Reference for the teaching of not-self

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



Four Colour Theorem



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?How many different game situations has connect four?$Z_n backslash {0}$ splits into octetsThe four colour theoremKempe's proof of the four colour theoremChessboard 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 theoremStrategies 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
    1 hour 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
    1 hour ago










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










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







Bor Kari

















asked 1 hour 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
    1 hour 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
    1 hour ago










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










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










1 Answer
1






active

oldest

votes


















4












$begingroup$

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
    56 mins ago










  • $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    26 mins 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%2ffour-colour-theorem%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









4












$begingroup$

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
    56 mins ago










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
















4












$begingroup$

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
    56 mins ago










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














4












4








4





$begingroup$

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 52 mins ago

























answered 1 hour 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
    56 mins ago










  • $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    26 mins 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
    56 mins ago










  • $begingroup$
    just curious -- did you write code to do this, or did you do this by hand?
    $endgroup$
    – antkam
    26 mins 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
56 mins ago




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












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




$begingroup$
just curious -- did you write code to do this, or did you do this by hand?
$endgroup$
– antkam
26 mins 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%2ffour-colour-theorem%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

El tren de la libertad Índice Antecedentes "Porque yo decido" Desarrollo de la...

Puerta de Hutt Referencias Enlaces externos Menú de navegación15°58′00″S 5°42′00″O /...

Castillo d'Acher Características Menú de navegación