TY - JOUR

T1 - Two more characterizations of König–Egerváry graphs

AU - Jarden, Adi

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

N1 - Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/11/20

Y1 - 2017/11/20

N2 - Let G be a simple graph with vertex set V(G). A set S⊆V(G) is independent if no two vertices from S are adjacent. The graph G is known to be König–Egerváry if α(G)+μ(G)=|V(G)|, where α(G) denotes the size of a maximum independent set and μ(G) is the cardinality of a maximum matching. A nonempty collection Γ of maximum independent sets is König–Egerváry if |⋃Γ|+|⋂Γ|=2α(G) (Jarden et al., 2015). In this paper, we prove that G is a König–Egerváry graph if and only if for every two maximum independent sets S1,S2 of G, there is a matching from V(G)−S1∪S2 into S1∩S2. Moreover, the same is true, when instead of two sets S1 and S2 we consider an arbitrary König–Egerváry collection.

AB - Let G be a simple graph with vertex set V(G). A set S⊆V(G) is independent if no two vertices from S are adjacent. The graph G is known to be König–Egerváry if α(G)+μ(G)=|V(G)|, where α(G) denotes the size of a maximum independent set and μ(G) is the cardinality of a maximum matching. A nonempty collection Γ of maximum independent sets is König–Egerváry if |⋃Γ|+|⋂Γ|=2α(G) (Jarden et al., 2015). In this paper, we prove that G is a König–Egerváry graph if and only if for every two maximum independent sets S1,S2 of G, there is a matching from V(G)−S1∪S2 into S1∩S2. Moreover, the same is true, when instead of two sets S1 and S2 we consider an arbitrary König–Egerváry collection.

KW - Core

KW - Corona

KW - König–Egerváry collection

KW - König–Egerváry graph

KW - Maximum independent set

KW - Maximum matching

UR - http://www.scopus.com/inward/record.url?scp=84977549704&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.05.012

DO - 10.1016/j.dam.2016.05.012

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AN - SCOPUS:84977549704

SN - 0166-218X

VL - 231

SP - 175

EP - 180

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -