Work

Hypergraphs with Polynomial Representation: Introducing $r$-splits

Year: 2024

Type: article

Abstract: 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 $\mathcal O(n^{r+1})$ of its hyperedges, despite its potentially exponential number of hyperedges. We also prove that there exist hypergraphs that need at least $\Omega(n^r)$ hyperedges to be represented, using a generalization of set orthogonality.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.10751

Authors: François Pitois, Mohammed Haddad, Hamida Seba, Olivier Togni

Institutions: Lyon 1 Université, Université de Bourgogne, Laboratoire d'Informatique en Images et Systèmes d'Information

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: COmpREssing networks and GRAPHs for efficIEnt computing