Onq-Power Cycles in Cubic Graphs

Julien Bensmail. "Onq-Power Cycles in Cubic Graphs." Discussiones Mathematicae Graph Theory 37.1 (2017): 211-220. <http://eudml.org/doc/288010>.

@article{JulienBensmail2017,
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 all 2-power cycles have length 4 only, or 8 only.},
author = {Julien Bensmail},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cubic graphs; q-power cycles; Erdős-Gyárfás conjecture; $q$-power cycles},
language = {eng},
number = {1},
pages = {211-220},
title = {Onq-Power Cycles in Cubic Graphs},
url = {http://eudml.org/doc/288010},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Julien Bensmail
TI - Onq-Power Cycles in Cubic Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 211
EP - 220
AB - 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.
LA - eng
KW - cubic graphs; q-power cycles; Erdős-Gyárfás conjecture; $q$-power cycles
UR - http://eudml.org/doc/288010
ER -