On q-power cycles in cubic graphs

1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : 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.

Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-01629942
Contributor : Julien Bensmail <>
Submitted on : Tuesday, November 7, 2017 - 7:57:02 AM
Last modification on : Tuesday, May 26, 2020 - 6:50:53 PM
Document(s) archivé(s) le : Thursday, February 8, 2018 - 12:49:14 PM

File

qpower-orbit.pdf
Files produced by the author(s)

Citation

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

Record views