On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor

Ján Karabáš; Edita Máčajová

On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor

Combinatorics 2026-05-12 v1

Authors: Ján Karabáš , Edita Máčajová

Abstract

Let $G$ be a cubic graph admitting a $2$ -factor consisting of exactly two odd circuits, and let the complementary $1$ -factor contain precisely three spokes (along with an arbitrary number of chords). We show that four perfect matchings can cover $G$ . As a consequence, $G$ fulfils the 7/5-Conjecture of Alon and Tarsi.

Keywords

cubic graph 4-cover 2-factor odd circuit perfect matching 7/5-Conjecture

Cite

@article{arxiv.2605.09475,
  title  = {On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor},
  author = {Ján Karabáš and Edita Máčajová},
  journal= {arXiv preprint arXiv:2605.09475},
  year   = {2026}
}

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