On the Erdős-Gyárfás Conjecture in Claw-Free Graphs

Abstract

The Erdős-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erdős-Gyárfás conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free graphs

Keywords

• erdős-gyárfás conjecture
• claw-free graphs
• cycles