Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $G$ be an undirected odd cycle. Let $f$ be a proper 3-coloring of $G$. If $w=v_1v_2...v_k$ is a walk on $k$ vertices of $G$, let $f(w)=f(v_1)f(v_2)...f(v_k)$. Let $W_k=\{f(w)|w$ is a walk on $k$ vertices in $G\}$. Let $|W_k|$ be the cardinality of $W_k$.

Is it true that $\lim_{k \to \infty} \frac{\log |W_k|}{k}=\log 2$ regardless of the order of $G$ and the choice of $f$?

Thank you.

share|cite|improve this question

1 Answer 1

up vote 1 down vote accepted

Certainly not. Take the coloring that is alternating black and white, except for a single red.

share|cite|improve this answer

Your Answer


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.