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 $ text42-COLOR $ is in NP and then I must reduce it from $ text3-COLOR $. Here it becomes complicated.
Is it similar to $ ktext-COLOR $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited Dec 16 at 14:51
xskxzr
3,4321730
asked Dec 16 at 11:37
gil
62
add a comment |
The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text42-COLOR $ is in NP and then I must reduce it from $ text3-COLOR $. Here it becomes complicated.
Is it similar to $ ktext-COLOR $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited Dec 16 at 14:51
xskxzr
3,4321730
asked Dec 16 at 11:37
gil
62
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27
add a comment |
The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text42-COLOR $ is in NP and then I must reduce it from $ text3-COLOR $. Here it becomes complicated.
Is it similar to $ ktext-COLOR $ for any $k$?
graphs graph-theory np-complete reductions colorings
edited Dec 16 at 14:51
xskxzr
3,4321730
asked Dec 16 at 11:37
gil
62
The requirement is that two adjacent vertices have different colors, and max. 42 colors.
I show that $ text42-COLOR $ is in NP and then I must reduce it from $ text3-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 Dec 16 at 14:51
xskxzr
3,4321730
asked Dec 16 at 11:37
gil
62
edited Dec 16 at 14:51
xskxzr
3,4321730
asked Dec 16 at 11:37
gil
62
edited Dec 16 at 14:51
xskxzr
3,4321730
edited Dec 16 at 14:51
xskxzr
3,4321730
edited Dec 16 at 14:51
xskxzr
3,4321730
3,4321730
asked Dec 16 at 11:37
gil
62
asked Dec 16 at 11:37
gil
62
asked Dec 16 at 11:37
gil
62
62
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27
add a comment |
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27
add a comment |
1 Answer
1
active
oldest
votes
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 Dec 16 at 14:55
xskxzr
3,4321730
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 Dec 16 at 14:55
xskxzr
3,4321730
add a comment |
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 Dec 16 at 14:55
xskxzr
3,4321730
add a comment |
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 Dec 16 at 14:55
xskxzr
3,4321730
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 Dec 16 at 14:55
xskxzr
3,4321730
answered Dec 16 at 14:55
xskxzr
3,4321730
answered Dec 16 at 14:55
xskxzr
3,4321730
answered Dec 16 at 14:55
xskxzr
3,4321730
3,4321730
add a comment |
add a comment |
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Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
Dec 16 at 12:00
The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
Dec 16 at 12:27