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Ear-Slicing for Matchings in Hypergraphs

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Abstract

We study when a given edge of a factor-critical graph is contained in a matching avoiding exactly one, pregiven vertex of the graph. We then apply the results to always partition the vertex-set of a 3-regular, 3-uniform hypergraph into at most one triangle (hyperedge of size 3) and edges (subsets of size 2 of hyperedges), corresponding to the intuition, and providing new insight to triangle and edge packings of Cornuéjols’ and Pulleyblank’s. The existence of such a packing can be considered to be a hypergraph variant of Petersen’s theorem on perfect matchings, and leads to a simple proof for a sharpening of Lu’s theorem on antifactors of graphs.

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References

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Acknowledgements

Many thanks to Zoltán Szigeti and Louis Esperet for precious suggestions!

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Authors and Affiliations

  1. CNRS, Laboratoire G-SCOP, Univ. Grenoble Alpes, Grenoble, France

    András Sebő

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  1. András Sebő
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Correspondence to András Sebő.

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Sebő, A. Ear-Slicing for Matchings in Hypergraphs. Graphs and Combinatorics 36, 1947–1951 (2020). https://doi.org/10.1007/s00373-020-02228-y

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  • DOI: https://doi.org/10.1007/s00373-020-02228-y

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