SOLVED
Is it true that for every infinite arithmetic progression $P$ which contains even numbers there is some constant $c=c(P)$ such that every graph with average degree at least $c$ contains a cycle whose length is in $P$?
In
[Er82e] Erdős credits this conjecture to himself and Burr. This has been proved by Bollobás
[Bo77]. The best dependence of the constant $c(P)$ is unknown.
See also [72].
