On the Erdős-Gyárfás conjecture for some Cayley graphs

M. Ghasemi, R. Varmazyar

In 1995, Paul Erdős and András Gyárfás conjectured that for every graph $X$ of minimum degree at least $3$, there exists a non-negative integer $m$ such that $X$ contains a simple cycle of length $2^m$. In this paper, we prove that the conjecture holds for Cayley graphs of order $2p^2$ and $4p$.