How to reduce 3-COLOR to 42-COLOR?
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The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.
Is it similar to $ ktext{-COLOR} $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited 3 hours ago
xskxzr
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asked 6 hours ago
gil
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up vote
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The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.
Is it similar to $ ktext{-COLOR} $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited 3 hours ago
xskxzr
3,3671730
asked 6 hours ago
gil
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.
Is it similar to $ ktext{-COLOR} $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited 3 hours ago
xskxzr
3,3671730
asked 6 hours ago
gil
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.
Is it similar to $ ktext{-COLOR} $ for any $k$?
graphs graph-theory np-complete reductions colorings
graphs graph-theory np-complete reductions colorings
edited 3 hours ago
xskxzr
3,3671730
asked 6 hours ago
gil
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
xskxzr
3,3671730
asked 6 hours ago
gil
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
xskxzr
3,3671730
edited 3 hours ago
xskxzr
3,3671730
edited 3 hours ago
xskxzr
3,3671730
3,3671730
asked 6 hours ago
gil
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
gil
62
asked 6 hours ago
gil
62
62
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago
add a comment |
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago
add a comment |
1 Answer
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For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.
answered 3 hours ago
xskxzr
3,3671730
add a comment |
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1 Answer
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1 Answer
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active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.
answered 3 hours ago
xskxzr
3,3671730
add a comment |
up vote
3
down vote
For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.
answered 3 hours ago
xskxzr
3,3671730
add a comment |
up vote
3
down vote
up vote
3
down vote
For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.
answered 3 hours ago
xskxzr
3,3671730
For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.
answered 3 hours ago
xskxzr
3,3671730
answered 3 hours ago
xskxzr
3,3671730
answered 3 hours ago
xskxzr
3,3671730
answered 3 hours ago
xskxzr
3,3671730
3,3671730
add a comment |
add a comment |
gil is a new contributor. Be nice, and check out our Code of Conduct.
gil is a new contributor. Be nice, and check out our Code of Conduct.
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Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago