PreprintarXiv licencearXiv
Ore-degree conditions for hypergraph matchings
Abstract
Let σk(H) be the minimum sum of the vertex degrees over all non-edges of an n-vertex k-uniform hypergraph H. For every k≥3, n≥ ks and sufficiently large n, we establish a sharp Ore-type degree condition that forces a matching of size s in H. Specifically, we prove that if σk(H)>max{ k(binomn−1k−1−binomn−sk−1), (k−c)binomks−2k−1}, then H has a matching of size s, where c=n−ks+1. In particular, this proves a conjecture of Balogh, Palmer and Raeisi for k≥ 3 and sufficiently large n.
Related
- Generalized Ramsey Numbers via Conflict-Free Hypergraph Matchings
- Perfect matchings in planar 3-connected graphs: girth five and minimum degree five
- Half-Optimal Induced Matchings in Random Graphs: Online and Low-Degree Algorithms
- Signless Laplacian spectral conditions for rainbow matchings in a collection of bipartite graphs
- Degree conditions for k-strong orientations of digraphs
BibTeX
@misc{guo2026oredegree,
title = {{Ore-degree conditions for hypergraph matchings}},
author = {Mingyang Guo and Tianhong Kan and Hongliang Lu and Feihong Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41787},
eprint = {2610.41787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41787},
}
RIS
TY - UNPB
TI - Ore-degree conditions for hypergraph matchings
AU - Mingyang Guo
AU - Tianhong Kan
AU - Hongliang Lu
AU - Feihong Yuan
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41787
UR - https://arxiv.org/abs/2610.41787
AB - Let σ_k(H) be the minimum sum of the vertex degrees over all non-edges of an n-vertex k-uniform hypergraph H. For every k≥3, n≥ ks and sufficiently large n, we establish a sharp Ore-type degree condition that forces a matching of size s in H. Specifically, we prove that if σ_k(H)>max{ k(binomn−1k−1−binomn−sk−1), (k−c)binomks−2k−1}, then H has a matching of size s, where c=n−ks+1. In particular, this proves a conjecture of Balogh, Palmer and Raeisi for k≥ 3 and sufficiently large n.
ER -