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

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?

Derivation tree not rendering

Four Colour Theorem

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

Does Parliament hold absolute power in the UK?

Is there a writing software that you can sort scenes like slides in PowerPoint?

What is this lever in Argentinian toilets?

Match Roman Numerals

Would an alien lifeform be able to achieve space travel if lacking in vision?

How is simplicity better than precision and clarity in prose?

Difference between "generating set" and free product?

Can withdrawing asylum be illegal?

Problems with Ubuntu mount /tmp

"... to apply for a visa" or "... and applied for a visa"?

Why can't wing-mounted spoilers be used to steepen approaches?

He got a vote 80% that of Emmanuel Macron’s

Why is superheterodyning better than direct conversion?

Is this wall load bearing? Blueprints and photos attached

Who or what is the being for whom Being is a question for Heidegger?

What LEGO pieces have "real-world" functionality?

does high air pressure throw off wheel balance?

Road tyres vs "Street" tyres for charity ride on MTB Tandem

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



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
    55 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
    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
    55 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 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
    55 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
    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
    55 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
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
55 mins ago




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










1 Answer
1






active

oldest

votes


















3












$begingroup$

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
    35 mins 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
    33 mins ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    29 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









3












$begingroup$

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
    35 mins 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
    33 mins ago










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















3












$begingroup$

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
    35 mins 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
    33 mins ago










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













3












3








3





$begingroup$

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 25 mins ago

























answered 59 mins 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
    35 mins 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
    33 mins ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    29 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
    35 mins 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
    33 mins ago










  • $begingroup$
    That's pretty good. A simple standard: at least one drivable road between neighbors
    $endgroup$
    – Will Jagy
    29 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
35 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
35 mins 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
33 mins 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
33 mins ago












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




$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
29 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

名間水力發電廠 目录 沿革 設施 鄰近設施 註釋 外部連結 导航菜单23°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.7113923°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.71139計畫概要原始内容臺灣第一座BOT 模式開發的水力發電廠-名間水力電廠名間水力發電廠 水利署首件BOT案原始内容《小檔案》名間電廠 首座BOT水力發電廠原始内容名間電廠BOT - 經濟部水利署中區水資源局

Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?

Is my guitar’s action too high? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strings too stiff on a recently purchased acoustic guitar | Cort AD880CEIs the action of my guitar really high?Μy little finger is too weak to play guitarWith guitar, how long should I give my fingers to strengthen / callous?When playing a fret the guitar sounds mutedPlaying (Barre) chords up the guitar neckI think my guitar strings are wound too tight and I can't play barre chordsF barre chord on an SG guitarHow to find to the right strings of a barre chord by feel?High action on higher fret on my steel acoustic guitar