Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871598 | Discrete Applied Mathematics | 2018 | 7 Pages |
Abstract
A matching in a hypergraph H is a set of pairwise disjoint hyperedges. The matching number ν(H) of H is the size of a maximum matching in H. A subset D of vertices of H is a dominating set of H if for every vâVâD there exists uâD such that u and v lie in an hyperedge of H. The cardinality of a minimum dominating set of H is the domination number of H, denoted by γ(H). It was proved that γ(H)â¤(râ1)ν(H) for r-uniform hypergraphs and the 2-uniform hypergraphs (graphs) achieving equality γ(H)=ν(H) have been characterized. In this paper we generalize the inequality γ(H)â¤(râ1)ν(H) to arbitrary hypergraph of rank r and we completely characterize the extremal hypergraphs H of rank 3 achieving equality γ(H)=(râ1)ν(H).
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Erfang Shan, Yanxia Dong, Liying Kang, Shan Li,