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Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2023

Hypergraphs with Polynomial Representation: Introducing r-splits

Résumé

Inspired by the split decomposition of graphs and rank-width, we introduce the notion of r-splits. We focus on the family of r-splits of a graph of order n, and we prove that it forms a hypergraph with several properties. We prove that such hypergraphs can be represented using only O(n r+1) of its hyperedges, despite its potentially exponential number of hyperedges. We also prove that there exist hypergraphs that need at least Ω(n r) hyperedges to be represented, using a generalization of set orthogonality.
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hal-04240302 , version 1 (13-10-2023)

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François Pitois, Mohammed Haddad, Hamida Seba, Olivier Togni. Hypergraphs with Polynomial Representation: Introducing r-splits. Discrete Mathematics and Theoretical Computer Science, inPress, special issue ICGT'22, 25:3, ⟨10.46298/dmtcs.10751⟩. ⟨hal-04240302⟩
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