Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903083 | Discrete Mathematics | 2018 | 11 Pages |
Abstract
A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. A d-matching in a 3-uniform hypergraph H is a matching of size d. Let V1,V2 be a partition of n vertices such that |V1|=2dâ1 and |V2|=nâ2d+1. Denote by E3(2dâ1,nâ2d+1) the 3-uniform hypergraph with vertex set V1âªV2 consisting of all those edges which contain at least two vertices of V1. Let H be a 3-uniform hypergraph of order nâ¥9d2 such that deg(u)+deg(v)>2[nâ12ânâd2] for any two adjacent vertices u,vâV(H). In this paper, we prove H contains a d-matching if and only if H is not a subgraph of E3(2dâ1,nâ2d+1).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yi Zhang, Mei Lu,