On $4$-perfect-matching covers of cubic graphs with two adjacent odd circuits in a $2$-factor
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Karabáš, Ján, Máčajová, Edita
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160908268