On the Erdős-Gyárfás conjecture in claw-free graphs

Details On the Erdős-Gyárfás conjecture in claw-free graphs On the Erdős-Gyárfás conjecture in claw-free graphs

2011-09-25

arxiv.org/abs/1109.5398v2

Mathematics

Combinatorics

6 pages. Some more details were added to the proofs

Scientific paper

The Erd\H{o}s-Gy\'arf\'as 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 shown itself far from reach, Hobbs asked if the Erd\H{o}s-Gy\'arf\'as conjecture holds in the claw-free case. In this paper, we obtain some results on this question. We also treat the Erd\H{o}s-Gy\'arf\'as conjecture in cubic claw-free graphs, together with posing a related conjecture and a problem.

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