TY - JOUR

T1 - Critical and maximum independent sets of a graph

AU - Jarden, Adi

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

N1 - Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Let G be a simple graph with vertex set VG. A set A⊆VG is independent if no two vertices from A are adjacent. If αG+μG=|VG|, then G is called a König–Egerváry graph (Deming, 1979; Sterboul, 1979), where αG is the size of a maximum independent set and μG stands for the cardinality of a largest matching in G. The number dX=X−N(X) is the difference of X⊆VG, and a set A⊆VG is critical if d(A)=max{dX:X⊆VG} (Zhang, 1990). In this paper, we present various connections between unions and intersections of maximum and/or critical independent sets of a graph, which lead to new characterizations of König–Egerváry graphs.

AB - Let G be a simple graph with vertex set VG. A set A⊆VG is independent if no two vertices from A are adjacent. If αG+μG=|VG|, then G is called a König–Egerváry graph (Deming, 1979; Sterboul, 1979), where αG is the size of a maximum independent set and μG stands for the cardinality of a largest matching in G. The number dX=X−N(X) is the difference of X⊆VG, and a set A⊆VG is critical if d(A)=max{dX:X⊆VG} (Zhang, 1990). In this paper, we present various connections between unions and intersections of maximum and/or critical independent sets of a graph, which lead to new characterizations of König–Egerváry graphs.

KW - Core

KW - Corona

KW - Critical set

KW - König–Egerváry graph

KW - Maximum independent set

UR - http://www.scopus.com/inward/record.url?scp=85046120867&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2018.03.058

DO - 10.1016/j.dam.2018.03.058

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AN - SCOPUS:85046120867

SN - 0166-218X

VL - 247

SP - 127

EP - 134

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -