Matching and domination numbers in r-uniform hypergraphs

Liying Kang (), Shan Li (), Yanxia Dong () and Erfang Shan ()
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Liying Kang: Shanghai University
Shan Li: Shanghai University
Yanxia Dong: Shanghai University
Erfang Shan: Shanghai University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 2, No 24, 656-659

Abstract: Abstract A matching is a set of pairwise disjoint hyperedges of a hypergraph H. The matching number $$\nu (H)$$ ν ( H ) of H is the maximum cardinality of a matching. A subset D of vertices of H is called a dominating set of H if for every vertex v not in D there exists $$u\in D$$ u ∈ D such that u and v are contained in a hyperedge of H. The minimum cardinality of a dominating set of H is called the domination number of H and is denoted by $$\gamma (H)$$ γ ( H ) . In this paper we show that every r-uniform hypergraph H satisfies the inequality $$\gamma (H)\le (r-1)\nu (H)$$ γ ( H ) ≤ ( r - 1 ) ν ( H ) and the bound is sharp.

Keywords: Hypergraph; Matching; Dominating set; Finite projective plane; Intersecting hypergraph (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10878-016-0098-5

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