Geodesic
On q-Power Cycles in Cubic Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 211-220

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In the context of a conjecture of Erdős and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e., with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning the remaining case q = 2 (which corresponds to the conjecture of Erdős and Gyárfás), we show that there exist arbitrarily large cubic graphs whose all 2-power cycles have length 4 only, or 8 only.
Keywords: cubic graphs, q -power cycles, Erdős-Gyárfás conjecture 
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Bensmail, Julien. On q-Power Cycles in Cubic Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 211-220. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a14/