Rotation snark, Berge-Fulkerson conjecture and Catlin’s 4-flow reduction

Siyan Liu, Rong-Xia Hao and Cun-Quan Zhang

Applied Mathematics and Computation, 2021, vol. 410, issue C

Abstract: It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. An infinite family R, of cyclically 5-edge-connected rotation snarks, was discovered in [European J. Combin. 2021] by Máčajová and Škoviera. In this paper, the Berge-Fulkerson conjecture is verified for the family R, and furthermore, a sup-family of R. Catlin’s contractible configuration and Tutte’s integer flow are applied here as the key methods.

Keywords: Berge-Fulkerson conjecture; Perfect matching; Snark; Rotation snark; 4-Circuit reduction (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005300

DOI: 10.1016/j.amc.2021.126441

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