Matroidal Cycles and Hypergraph Families
Combinatorics
2024-11-01 v1
Abstract
We propose a novel definition of hypergraphical matroids, defined for arbitrary hypergraphs, simultaneously generalizing previous definitions for regular hypergraphs (Main, 1978), and for the hypergraphs of circuits of a matroid (Freij-Hollanti, Jurrius, Kuznetsova, 2023). As a consequence, we obtain a new notion of cycles in hypergraphs, and hypertrees. We give an equivalence relation on hypergraphs, according to when their so-called matroidal closures agree. Finally, we characterize hypergraphs that are isomorphic to the circuit hypergraphs of the associated matroids.
Keywords
Cite
@article{arxiv.2410.23932,
title = {Matroidal Cycles and Hypergraph Families},
author = {Ragnar Freij-Hollanti and Patricija Šapokaitė},
journal= {arXiv preprint arXiv:2410.23932},
year = {2024}
}