A Characterization of König-Egerváry Graphs Using a Common Property of All Maximum Matchings

Vadim E. Levit; Eugen Mandrescu

doi:10.1016/j.endm.2011.09.092

A Characterization of König-Egerváry Graphs Using a Common Property of All Maximum Matchings

Vadim E. Levit
, Eugen Mandrescu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The independence number of a graph G, denoted by α(G), is the cardinality of an independent set of maximum size in G, while μ(G) is the size of a maximum matching in G, i.e., its matching number. G is a König-Egerváry graph if its order equals α(G) + μ(G). In this paper we give a new characterization of König-Egerváry graphs. We also deduce some properties of vertices belonging to all maximum independent sets of a König-Egerváry graph.

Original language	English
Pages (from-to)	565-570
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	38
DOIs	https://doi.org/10.1016/j.endm.2011.09.092
State	Published - 1 Dec 2011

Keywords

Core
Maximum independent set
Maximum matching

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10.1016/j.endm.2011.09.092

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abstract = "The independence number of a graph G, denoted by α(G), is the cardinality of an independent set of maximum size in G, while μ(G) is the size of a maximum matching in G, i.e., its matching number. G is a K{\"o}nig-Egerv{\'a}ry graph if its order equals α(G) + μ(G). In this paper we give a new characterization of K{\"o}nig-Egerv{\'a}ry graphs. We also deduce some properties of vertices belonging to all maximum independent sets of a K{\"o}nig-Egerv{\'a}ry graph.",

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N2 - The independence number of a graph G, denoted by α(G), is the cardinality of an independent set of maximum size in G, while μ(G) is the size of a maximum matching in G, i.e., its matching number. G is a König-Egerváry graph if its order equals α(G) + μ(G). In this paper we give a new characterization of König-Egerváry graphs. We also deduce some properties of vertices belonging to all maximum independent sets of a König-Egerváry graph.

AB - The independence number of a graph G, denoted by α(G), is the cardinality of an independent set of maximum size in G, while μ(G) is the size of a maximum matching in G, i.e., its matching number. G is a König-Egerváry graph if its order equals α(G) + μ(G). In this paper we give a new characterization of König-Egerváry graphs. We also deduce some properties of vertices belonging to all maximum independent sets of a König-Egerváry graph.

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KW - Maximum independent set

KW - Maximum matching

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ER -

A Characterization of König-Egerváry Graphs Using a Common Property of All Maximum Matchings

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Keywords

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