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Four Colour Theorem
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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
asked 1 hour ago
Bor KariBor Kari
3749
$endgroup$
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
asked 1 hour ago
Bor KariBor Kari
3749
$endgroup$
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
45 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
asked 1 hour ago
Bor KariBor Kari
3749
$endgroup$
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
asked 1 hour ago
Bor KariBor Kari
3749
asked 1 hour ago
Bor KariBor Kari
3749
edited 59 mins ago
Bor Kari
asked 1 hour ago
Bor KariBor Kari
3749
asked 1 hour ago
Bor KariBor Kari
3749
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
45 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
1 hour ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
45 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
45 mins ago
$begingroup$
thank you for your suggestion, I made a few clarifications.
$endgroup$
– Bor Kari
45 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.
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
$endgroup$
$begingroup$
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
25 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 mins ago
add a comment |
Your Answer
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1 Answer
1
active
oldest
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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.
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
$endgroup$
$begingroup$
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
25 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 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.
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
$endgroup$
$begingroup$
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
25 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 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.
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
$endgroup$
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.
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
edited 15 mins ago
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
answered 49 mins ago
Misha LavrovMisha Lavrov
49.3k757108
answered 49 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
25 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 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
25 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– 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
25 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
25 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
23 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
23 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 mins ago
$begingroup$
That's pretty good. A simple standard: at least one drivable road between neighbors
$endgroup$
– Will Jagy
19 mins ago
add a comment |
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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
45 mins ago