Show that the 3-color problem is in P when the input graph is a tree.












0












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Every tree is $2$-colorable, so I'm not quite getting the question.
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:09










  • $begingroup$
    yeah I know but thats what the question states. I have no clue.
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:11
















0












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Every tree is $2$-colorable, so I'm not quite getting the question.
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:09










  • $begingroup$
    yeah I know but thats what the question states. I have no clue.
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:11














0












0








0





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 29 '18 at 21:41









gt6989b

33.6k22453




33.6k22453










asked Nov 29 '18 at 21:06









r4dicalbuRnr4dicalbuRn

31




31








  • 2




    $begingroup$
    Every tree is $2$-colorable, so I'm not quite getting the question.
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:09










  • $begingroup$
    yeah I know but thats what the question states. I have no clue.
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:11














  • 2




    $begingroup$
    Every tree is $2$-colorable, so I'm not quite getting the question.
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:09










  • $begingroup$
    yeah I know but thats what the question states. I have no clue.
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:11








2




2




$begingroup$
Every tree is $2$-colorable, so I'm not quite getting the question.
$endgroup$
– Cheerful Parsnip
Nov 29 '18 at 21:09




$begingroup$
Every tree is $2$-colorable, so I'm not quite getting the question.
$endgroup$
– Cheerful Parsnip
Nov 29 '18 at 21:09












$begingroup$
yeah I know but thats what the question states. I have no clue.
$endgroup$
– r4dicalbuRn
Nov 29 '18 at 21:11




$begingroup$
yeah I know but thats what the question states. I have no clue.
$endgroup$
– r4dicalbuRn
Nov 29 '18 at 21:11










1 Answer
1






active

oldest

votes


















1












$begingroup$

UPDATED following a suggestion in the comments.




  1. Validate that the input is a tree

  2. Answer "yes"


Both (1) and (2) are doable in polynomial time (how?) so this is in $P$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:33










  • $begingroup$
    @semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:40








  • 1




    $begingroup$
    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.)
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:41










  • $begingroup$
    @CheerfulParsnip :-) +1, funny, yes, definitely
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:43








  • 1




    $begingroup$
    @semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:47











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

UPDATED following a suggestion in the comments.




  1. Validate that the input is a tree

  2. Answer "yes"


Both (1) and (2) are doable in polynomial time (how?) so this is in $P$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:33










  • $begingroup$
    @semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:40








  • 1




    $begingroup$
    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.)
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:41










  • $begingroup$
    @CheerfulParsnip :-) +1, funny, yes, definitely
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:43








  • 1




    $begingroup$
    @semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:47
















1












$begingroup$

UPDATED following a suggestion in the comments.




  1. Validate that the input is a tree

  2. Answer "yes"


Both (1) and (2) are doable in polynomial time (how?) so this is in $P$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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?
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:33










  • $begingroup$
    @semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:40








  • 1




    $begingroup$
    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.)
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:41










  • $begingroup$
    @CheerfulParsnip :-) +1, funny, yes, definitely
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:43








  • 1




    $begingroup$
    @semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:47














1












1








1





$begingroup$

UPDATED following a suggestion in the comments.




  1. Validate that the input is a tree

  2. Answer "yes"


Both (1) and (2) are doable in polynomial time (how?) so this is in $P$






share|cite|improve this answer











$endgroup$



UPDATED following a suggestion in the comments.




  1. Validate that the input is a tree

  2. Answer "yes"


Both (1) and (2) are doable in polynomial time (how?) so this is in $P$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 29 '18 at 21:43

























answered Nov 29 '18 at 21:27









gt6989bgt6989b

33.6k22453




33.6k22453












  • $begingroup$
    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?
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:33










  • $begingroup$
    @semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:40








  • 1




    $begingroup$
    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.)
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:41










  • $begingroup$
    @CheerfulParsnip :-) +1, funny, yes, definitely
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:43








  • 1




    $begingroup$
    @semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:47


















  • $begingroup$
    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?
    $endgroup$
    – r4dicalbuRn
    Nov 29 '18 at 21:33










  • $begingroup$
    @semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:40








  • 1




    $begingroup$
    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.)
    $endgroup$
    – Cheerful Parsnip
    Nov 29 '18 at 21:41










  • $begingroup$
    @CheerfulParsnip :-) +1, funny, yes, definitely
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:43








  • 1




    $begingroup$
    @semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
    $endgroup$
    – gt6989b
    Nov 29 '18 at 21:47
















$begingroup$
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?
$endgroup$
– r4dicalbuRn
Nov 29 '18 at 21:33




$begingroup$
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?
$endgroup$
– r4dicalbuRn
Nov 29 '18 at 21:33












$begingroup$
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
$endgroup$
– gt6989b
Nov 29 '18 at 21:40






$begingroup$
@semal259 any 2-coloring is also a 3-coloring, so it does indeed prove that 3-coloring a tree is in $P$
$endgroup$
– gt6989b
Nov 29 '18 at 21:40






1




1




$begingroup$
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.)
$endgroup$
– Cheerful Parsnip
Nov 29 '18 at 21:41




$begingroup$
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.)
$endgroup$
– Cheerful Parsnip
Nov 29 '18 at 21:41












$begingroup$
@CheerfulParsnip :-) +1, funny, yes, definitely
$endgroup$
– gt6989b
Nov 29 '18 at 21:43






$begingroup$
@CheerfulParsnip :-) +1, funny, yes, definitely
$endgroup$
– gt6989b
Nov 29 '18 at 21:43






1




1




$begingroup$
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
$endgroup$
– gt6989b
Nov 29 '18 at 21:47




$begingroup$
@semal259 Indeed, a tree is $k$-colorable in polynomial time for all $k ge 2$.
$endgroup$
– gt6989b
Nov 29 '18 at 21:47


















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