Take the 2-minute tour ×  I know how to work out the chromatic
polynomial of a graph and I can work out what $k$ would be by
looking at the graph. Maybe I'm just being silly, but if you
were given just the chromatic polynomial say: $$ k(k-1)^2 (k-2)
$$ can you just look at that and tell that the chromatic number
of $G$ is $3$?  share|improve this question What is $k$? It's
not clear from the question. –  Thomas Andrews Dec 7 '12 at
14:51 Yes, is it supposed to be chromatic number? –  Simon
Hayward Dec 7 '12 at 15:01 Yeah the chromatic number, sorry I
should of said! –  Jack Dec 7 '12 at 15:02 add comment  1 Answer
up vote 1 down vote accepted  If $p(k)$ is the chromatic
polynomial of $G$, then the chromatic number of $G$ is the
smallest non-negative integer $k_0$ such that $p(k_0)>0$.  In
this case, you can clearly see that $p(0)=p(1)=p(2)=0$, while
$p(3)\neq 0$, so the chromatic number must be $3$.
share|improve this answer Thank you! My lecture notes have
totally just skipped that –  Jack Dec 7 '12 at 15: