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.
Highlights
The cardinality [8] of a finite set V is denoted by | V |
The problem of identifying the minimal transversals in a given hypergraph H will be denoted by HY P − T RAN S − H, and the problem of identifying the minimal dominating sets in H will be denoted by HY P − DOM − H
If Y ∈ 2V ∗, Y is a solution to HY P − T RAN S − H if Y is a minimal transversal in H
Summary
The cardinality (or, size) [8] of a finite set V is denoted by | V |. A simple hypergraph [2] is an ordered couple H = (V, E) where: (i) V is a nonempty finite set and (ii) E is a set of nonempty subsets of V such that. The problem of identifying the minimal transversals in a given hypergraph H will be denoted by HY P − T RAN S − H, and the problem of identifying the minimal dominating sets in H will be denoted by HY P − DOM − H. Y is a solution to HY P − DOM − H (written Y ∈ HY P − DOM − H) if Y is a minimal dominating set in H. The hypergraphs considered in this article are all assumed loop-free and of the Sperner type.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Pure and Apllied Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
