A characterization of Konig-Egervary graphs using a common property of all maximum matchings
Vadim E. Levit, Eugen Mandrescu
TL;DR
This paper introduces a new characterization of Konig-Egervary graphs based on properties of maximum matchings and independent sets, enhancing understanding of their structural properties.
Contribution
It provides a novel characterization of Konig-Egervary graphs and explores properties of vertices in all maximum independent sets within these graphs.
Findings
New characterization of Konig-Egervary graphs
Properties of vertices in all maximum independent sets
Insights into the structure of maximum matchings
Abstract
The independence number of a graph G, denoted by alpha(G), is the cardinality of an independent set of maximum size in G, while mu(G) is the size of a maximum matching in G, i.e., its matching number. G is a Konig-Egervary graph if its order equals alpha(G)+mu(G). In this paper we give a new characterization of Konig-Egervary graphs. We also deduce some properties of vertices belonging to all maximum independent sets of a Konig-Egervary graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Commutative Algebra and Its Applications · Limits and Structures in Graph Theory