On covering cubic graphs with three perfect matchings

Fuente: arXiv
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Main Authors: Máčajová, Edita, Mazák, Ján
Format: Preprint
Published: 2025
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author Máčajová, Edita
Mazák, Ján
author_facet Máčajová, Edita
Mazák, Ján
contents For a bridgeless cubic graph $G$, $m_3(G)$ is the ratio of the maximum number of edges of $G$ covered by the union of $3$ perfect matchings to $|E(G)|$. We prove that for any $r\in [4/5, 1)$, there exist infinitely many cubic graphs $G$ such that $m_3(G) = r$. For any $r\in [9/10, 1)$, there exist infinitely many cyclically $4$-connected cubic graphs $G$ with $m_3(G) = r$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_05501
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On covering cubic graphs with three perfect matchings
Máčajová, Edita
Mazák, Ján
Combinatorics
Discrete Mathematics
05C70
For a bridgeless cubic graph $G$, $m_3(G)$ is the ratio of the maximum number of edges of $G$ covered by the union of $3$ perfect matchings to $|E(G)|$. We prove that for any $r\in [4/5, 1)$, there exist infinitely many cubic graphs $G$ such that $m_3(G) = r$. For any $r\in [9/10, 1)$, there exist infinitely many cyclically $4$-connected cubic graphs $G$ with $m_3(G) = r$.
title On covering cubic graphs with three perfect matchings
topic Combinatorics
Discrete Mathematics
05C70
url https://arxiv.org/abs/2509.05501