Resolving a conjecture of Bollobás and Erdös, Gyárfás proved that every graph $G$ of chromatic number $k+1\geq 3$ contains cycles of $\lfloor\frac{k}{2}\rfloor$ distinct odd lengths. We strengthen this prominent result by showing that such $G$ contains cycles of $\lfloor\frac{k}{2}\rfloor$ consecutive odd lengths. Along the way, combining extremal and structural tools, we prove a stronger statement that every graph of chromatic number $k+1\geq 7$ contains $k$ cycles of consecutive lengths, except that some block is $K_{k+1}$. As corollaries, this confirms a conjecture of Verstraëte and answers a question of Moore and West when $k\geq6$.

Answering a question of Häggkvist and Scott, Verstraëte proved that every sufficiently large graph with average degree at least $k^2+19k+10$ contains $k$ vertex-disjoint cycles of consecutive even lengths. He further conjectured that the same holds for every graph $G$ with average degree at least $k^2+3k+2$. In this paper we prove this conjecture for $k\geq 19$ when $G$ is sufficiently large. We also show that for any $\epsilon>0$ and large $k\geq k_\epsilon$, average degree at least $k^2+3k-2+\epsilon$ suffices, which is asymptotically tight for infinitely many graphs.