Abstract

In 1995, Paul Erd\H{o}s 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 $4p$.

Keywords: Erd\H{o}s-Gyárf\'s conjecture; Cayley graphs; cycles of graphs.

MSC: 05C38, 20B25

Pages:  37$-$42     

Volume  73 ,  Issue  1 ,  2021