Degree and regularity of Eulerian ideals of hypergraphs
Commutative Algebra
2022-02-16 v1 Combinatorics
Abstract
We define the Eulerian ideal of a -uniform hypergraph and study its degree and Castelnuovo--Mumford regularity. The main tool is a Gr\"obner basis of the ideal obtained combinatorially from the hypergraph. We define the notion of parity join in a hypergraph and show that the regularity of the Eulerian ideal is equal to the maximum cardinality of such a set of edges. The formula for the degree involves the cardinality of the set of sets of vertices, , that admit a -join. We compute the degree and regularity explicity in the cases of a complete -partite hypergraph and a complete hypergraph of rank .
Keywords
Cite
@article{arxiv.2202.07000,
title = {Degree and regularity of Eulerian ideals of hypergraphs},
author = {J. Neves and G. Varejão},
journal= {arXiv preprint arXiv:2202.07000},
year = {2022}
}