ON THE ERD\H{O}S-GYÁRFÁS CONJECTURE FOR SOME CAYLEY GRAPHS
M. Ghasemi, R. Varmazyar
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 2m.
In this paper, we prove that the conjecture holds for Cayley graphs of order 2p2 and 4p.
Keywords: Erd\H{o}s-Gyárf\'s conjecture; Cayley graphs; cycles of graphs.