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
What do you call a plan that's an alternative plan in case your initial plan fails?
how can a perfect fourth interval be considered either consonant or dissonant?
Segmentation fault output is suppressed when piping stdin into a function. Why?
Why is superheterodyning better than direct conversion?
Was credit for the black hole image misattributed?
Does Parliament need to approve the new Brexit delay to 31 October 2019?
What can I do if neighbor is blocking my solar panels intentionally?
Sort a list of pairs representing an acyclic, partial automorphism
The following signatures were invalid: EXPKEYSIG 1397BC53640DB551
Road tyres vs "Street" tyres for charity ride on MTB Tandem
Are my PIs rude or am I just being too sensitive?
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
How many people can fit inside Mordenkainen's Magnificent Mansion?
Why can't wing-mounted spoilers be used to steepen approaches?
Difference between "generating set" and free product?
Four Colour Theorem
How to test the equality of two Pearson correlation coefficients computed from the same sample?
Match Roman Numerals
How do I add random spotting to the same face in cycles?
Single author papers against my advisor's will?
Why is the object placed in the middle of the sentence here?
I could not break this equation. Please help me
Mortgage adviser recommends a longer term than necessary combined with overpayments
How to split my screen on my Macbook Air?
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
$begingroup$
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).
graph-theory recreational-mathematics
$endgroup$
add a comment |
$begingroup$
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).
graph-theory recreational-mathematics
$endgroup$
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
59 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 mins ago
add a comment |
$begingroup$
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).
graph-theory recreational-mathematics
$endgroup$
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
graph-theory recreational-mathematics
edited 53 mins 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
59 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 mins ago
add a comment |
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
59 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 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
59 mins 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
59 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 mins ago
add a comment |
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.
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:
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
19 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
add a comment |
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%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
$begingroup$
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:
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
19 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
add a comment |
$begingroup$
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:
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
19 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
add a comment |
$begingroup$
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:
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.
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:
Adjacencies between the states may be easier to see here.
edited 9 mins ago
answered 43 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
19 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
add a comment |
$begingroup$
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
19 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 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
19 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
19 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
17 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
17 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
13 mins ago
add a comment |
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%2ffour-colour-theorem%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
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
59 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
39 mins ago