On q-power cycles in cubic graphs

Julien Bensmail (1)

1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications

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 only 2-power cycles have length 4 only, or 8 only.

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail. On q-power cycles in cubic graphs. Discussiones Mathematicae Graph Theory, 2017, 37 (1), pp.211 - 220. ⟨10.7151/dmgt.1926⟩. ⟨hal-01629942⟩