Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In other words, can a planar graph without k3 have a chromatic number larger than 3?

share|improve this question

1 Answer 1

up vote 3 down vote accepted

Yes, every triangle-free planar graph is 3-colorable. This is known as Grötzsch's theorem.

share|improve this answer
1  
It is perhaps worth noting that the theorem does not generalize in the natural way, as evidenced in answers to this question: math.stackexchange.com/questions/225872/… –  Austin Mohr Nov 1 '12 at 2:58

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.