On the Erd\H{o}s-Gy\'arf\'as conjecture in claw-free graphs
Combinatorics
2013-02-08 v3
Abstract
The Erd\H{o}s-Gy\'{a}rf\'{a}s 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 Erd\H{o}s-Gy\'{a}rf\'{a}s conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free graphs.
Keywords
Cite
@article{arxiv.1109.5398,
title = {On the Erd\H{o}s-Gy\'arf\'as conjecture in claw-free graphs},
author = {Pouria Salehi Nowbandegani and Hossein Esfandiari and Mohammad Hassan Shirdareh Haghighi and Khodakhast Bibak},
journal= {arXiv preprint arXiv:1109.5398},
year = {2013}
}
Comments
Final version. Discussiones Mathematicae Graph Theory, to appear