On q-power cycles in cubic graphs

Julien Bensmail

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Abstract

In the context of a conjecture of Erdos 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 Erdos and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only.
Original languageEnglish
JournalDiscussiones Mathematicae. Graph Theory
Volume37
Pages (from-to)211–220
ISSN1234-3099
DOIs
Publication statusPublished - 2017

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