TY - JOUR

T1 - When is G 2 a König-Egerváry Graph?

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2013/9

Y1 - 2013/9

N2 - The independence number of a graph G, denoted by α(G), is the cardinality of a maximum independent set, and μ(G) is the size of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. The square of a graph G is the graph G 2 with the same vertex set as in G, and an edge of G 2 is joining two distinct vertices, whenever the distance between them in G is at most two. G is a square-stable graph if it enjoys the property α(G) = α(G 2). In this paper we show that G 2 is a König-Egerváry graph if and only if G is a square-stable König-Egerváry graph.

AB - The independence number of a graph G, denoted by α(G), is the cardinality of a maximum independent set, and μ(G) is the size of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. The square of a graph G is the graph G 2 with the same vertex set as in G, and an edge of G 2 is joining two distinct vertices, whenever the distance between them in G is at most two. G is a square-stable graph if it enjoys the property α(G) = α(G 2). In this paper we show that G 2 is a König-Egerváry graph if and only if G is a square-stable König-Egerváry graph.

KW - Maximum independent set

KW - Perfect matching

KW - Square of a graph

UR - http://www.scopus.com/inward/record.url?scp=84882832416&partnerID=8YFLogxK

U2 - 10.1007/s00373-012-1196-5

DO - 10.1007/s00373-012-1196-5

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AN - SCOPUS:84882832416

SN - 0911-0119

VL - 29

SP - 1453

EP - 1458

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 5

M1 - 5

ER -