Ear-Slicing for Matchings in Hypergraphs
Discrete Mathematics
2019-12-12 v1 Combinatorics
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 -regular, -uniform hypergraph into at most one triangle (hyperedge of size ) and edges (subsets of size of hyperedges), corresponding to the intuition, and providing new insight to triangle and edge packings of Cornu\'ejols' 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.
Cite
@article{arxiv.1912.05486,
title = {Ear-Slicing for Matchings in Hypergraphs},
author = {András Sebő},
journal= {arXiv preprint arXiv:1912.05486},
year = {2019}
}