Show that the 3-color problem is in P when the input graph is a tree.
0
This one is from university assignment. I am completely stuck on this one and I searched the internet but couldn't find a explanation.
Show that the 3-color problem is in P when the input graph is a tree.
Any explanation would be appreciated.
graph-theory computational-complexity coloring np-complete
edited Nov 29 at 21:41
gt6989b
33k22452
asked Nov 29 at 21:06
semal259
31
add a comment |
0
This one is from university assignment. I am completely stuck on this one and I searched the internet but couldn't find a explanation.
Show that the 3-color problem is in P when the input graph is a tree.
Any explanation would be appreciated.
graph-theory computational-complexity coloring np-complete
edited Nov 29 at 21:41
gt6989b
33k22452
asked Nov 29 at 21:06
semal259
31
2
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11
add a comment |
0
0
0
This one is from university assignment. I am completely stuck on this one and I searched the internet but couldn't find a explanation.
Show that the 3-color problem is in P when the input graph is a tree.
Any explanation would be appreciated.
graph-theory computational-complexity coloring np-complete
edited Nov 29 at 21:41
gt6989b
33k22452
asked Nov 29 at 21:06
semal259
31
This one is from university assignment. I am completely stuck on this one and I searched the internet but couldn't find a explanation.
Show that the 3-color problem is in P when the input graph is a tree.
Any explanation would be appreciated.
graph-theory computational-complexity coloring np-complete
graph-theory computational-complexity coloring np-complete
edited Nov 29 at 21:41
gt6989b
33k22452
asked Nov 29 at 21:06
semal259
31
edited Nov 29 at 21:41
gt6989b
33k22452
asked Nov 29 at 21:06
semal259
31
edited Nov 29 at 21:41
gt6989b
33k22452
edited Nov 29 at 21:41
gt6989b
33k22452
edited Nov 29 at 21:41
gt6989b
33k22452
33k22452
asked Nov 29 at 21:06
semal259
31
asked Nov 29 at 21:06
semal259
31
asked Nov 29 at 21:06
semal259
31
31
2
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11
add a comment |
2
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11
2
2
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11
add a comment |
1 Answer
1
active
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UPDATED following a suggestion in the comments.
- Validate that the input is a tree
- Answer "yes"
Both (1) and (2) are doable in polynomial time (how?) so this is in $P$
answered Nov 29 at 21:27
gt6989b
33k22452
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
|
show 2 more comments
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1 Answer
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UPDATED following a suggestion in the comments.
- Validate that the input is a tree
- Answer "yes"
Both (1) and (2) are doable in polynomial time (how?) so this is in $P$
answered Nov 29 at 21:27
gt6989b
33k22452
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
|
show 2 more comments
1
UPDATED following a suggestion in the comments.
- Validate that the input is a tree
- Answer "yes"
Both (1) and (2) are doable in polynomial time (how?) so this is in $P$
answered Nov 29 at 21:27
gt6989b
33k22452
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
|
show 2 more comments
1
1
1
UPDATED following a suggestion in the comments.
- Validate that the input is a tree
- Answer "yes"
Both (1) and (2) are doable in polynomial time (how?) so this is in $P$
answered Nov 29 at 21:27
gt6989b
33k22452
UPDATED following a suggestion in the comments.
- Validate that the input is a tree
- Answer "yes"
Both (1) and (2) are doable in polynomial time (how?) so this is in $P$
answered Nov 29 at 21:27
gt6989b
33k22452
edited Nov 29 at 21:43
answered Nov 29 at 21:27
gt6989b
33k22452
answered Nov 29 at 21:27
gt6989b
33k22452
answered Nov 29 at 21:27
gt6989b
33k22452
33k22452
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
|
show 2 more comments
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
Does this prove that 3-color is in P? 2-coloring can be done by BFS and tree is a bipartite by definition. But what about 3-color?
– semal259
Nov 29 at 21:33
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
– gt6989b
Nov 29 at 21:40
1
1
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
One could argue that it's even simpler than this, since the $2$-color problem should have a yes/no answer. Just write a program that always produces the answer yes (possibly after verifying that the input is a tree.)
– Cheerful Parsnip
Nov 29 at 21:41
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
@CheerfulParsnip :-) +1, funny, yes, definitely
– gt6989b
Nov 29 at 21:43
1
1
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
– gt6989b
Nov 29 at 21:47
|
show 2 more comments
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2
Every tree is $2$-colorable, so I'm not quite getting the question.
– Cheerful Parsnip
Nov 29 at 21:09
yeah I know but thats what the question states. I have no clue.
– semal259
Nov 29 at 21:11