Bounding the edge cover of a hypergraph
Farhad Shahrokhi

TL;DR
This paper establishes bounds on the minimum edge cover size of hypergraphs using the mighty degeneracy parameter, with proofs of tightness and applications in domination theory.
Contribution
It introduces the mighty degeneracy as a new parameter to bound edge covers in hypergraphs, providing tight inequalities and demonstrating applications.
Findings
Bound c(H) by mighty degeneracy and edge cover size
Proved the inequality is tight
Applied results to domination theory
Abstract
Let be a hypergraph. Let , then is an {\it edge cover}, or a {\it set cover}, if . A subset of vertices is {\it independent} in if no two vertices in are in any edge. Let and denote the cardinalities of a smallest edge cover and largest independent set in , respectively. We show that , where is a parameter called the {\it mighty degeneracy} of . Furthermore, we show that the inequality is tight and demonstrate the applications in domination theory.
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Taxonomy
TopicsMachine Learning and Algorithms · Computational Geometry and Mesh Generation · Optimization and Search Problems
