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A Class of Cubic Graphs Satisfying Berge Conjecture

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Abstract

Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for bridgeless cubic graphs which have two perfect matchings with at most one common edge.

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Funding

This work is supported by NSFC (Grant nos. 11701332 and 12061047) and by Jiangxi Provincial Natural Science Foundation (nos: 20212BAB201027 and 20192BAB211002).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University (Weihai), Weihai, 264209, Shandong, China

    Wuyang Sun

  2. School of Sciences, Nanchang University, Nanchang, 330000, Jiangxi, China

    Fan Wang

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  1. Wuyang Sun
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  2. Fan Wang
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Correspondence to Wuyang Sun.

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Sun, W., Wang, F. A Class of Cubic Graphs Satisfying Berge Conjecture. Graphs and Combinatorics 38, 66 (2022). https://doi.org/10.1007/s00373-022-02466-2

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  • DOI: https://doi.org/10.1007/s00373-022-02466-2

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