IJPAM: Volume 94, No. 3 (2014)
PROBLEMS IN HYPERGRAPH THEORY
Department of Mathematics
Thanjavur, Tamilnadu State, INDIA
Abstract. The problems of enumerating (i) all the minimal transversals and (ii) all the minimal dominating sets, in a given hypergraph, have received a lot of attention because of their applications in Computer Science. This article explores the possibilities of these two problems being solution-wise equivalent - that is, each solution to one of them being a solution to the other - in the domain of Sperner hypergraphs, culminating in identifying the only class of such hypergraphs in which the equivalence holds.
Received: January 2, 2014
AMS Subject Classification: 05C65
Key Words and Phrases: hypergraph, hyperedge, Sperner hypergraphs, trim hypergraph, transversal, dominating set
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DOI: 10.12732/ijpam.v94i3.6 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 373 - 377
This work is licensed under the Creative Commons Attribution International License (CC BY).