Geodesic
On the Erdős-Gyárfás conjecture in claw-free graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 635-640

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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 
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Nowbandegani, Pouria Salehi; Esfandiari, Hossein; Haghighi, Mohammad Hassan Shirdareh; Bibak, Khodakhast. On the Erdős-Gyárfás conjecture in claw-free graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 635-640. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a16/