What type of study is this?

This is a Quantitative Study study.

October 12, 2025Open Access

On covering cubic graphs with 3 perfect matchings

Key Points

The study determines that infinitely many cubic graphs exist for any r between 4/5 and 1, with m3(G) equaling r.
Graphs with m3(G) values in the range of 9/10 to 1 can be cyclically 4-connected and equally infinite.
Understanding the ratios of covered edges with perfect matchings enriches graph theory applications.
Results highlight specific constructions of graphs that meet the criteria, expanding existing knowledge.

Abstract

For a bridgeless cubic graph G, m₃ (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 [4/5, 1), there exist infinitely many cubic graphs G such that m₃ (G) = r. For any r [9/10, 1), there exist infinitely many cyclically 4-connected cubic graphs G with m₃ (G) = r.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Máčajová et al. (Fri,) studied this question.

synapsesocial.com/papers/68ec384042a190b2c35198b4 https://doi.org/https://doi.org/10.48550/arxiv.2509.05501