TY - GEN

T1 - On duality between local maximum stable sets of a graph and its line-graph

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

PY - 2009

Y1 - 2009

N2 - G is a König-Egervá ry graph provided α(G)+μ(G) = |V (G)|, where μ(G) is the size of a maximum matching and α(G) is the cardinality of a maximum stable set,[2],[21]. S is a local maximum stable set of G, and we write S ∈Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S,[11]. Nemhauser and Trotter Jr. proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G,[19]. In this paper we demonstrate that if S∈ Ψ(G), the subgraph H induced by S ∪ N(S) is a König-Egerváry graph, and M is a maximum matching in H, then M is a local maximum stable set in the line graph of G.

AB - G is a König-Egervá ry graph provided α(G)+μ(G) = |V (G)|, where μ(G) is the size of a maximum matching and α(G) is the cardinality of a maximum stable set,[2],[21]. S is a local maximum stable set of G, and we write S ∈Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S,[11]. Nemhauser and Trotter Jr. proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G,[19]. In this paper we demonstrate that if S∈ Ψ(G), the subgraph H induced by S ∪ N(S) is a König-Egerváry graph, and M is a maximum matching in H, then M is a local maximum stable set in the line graph of G.

UR - http://www.scopus.com/inward/record.url?scp=70249088033&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02029-2_12

DO - 10.1007/978-3-642-02029-2_12

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AN - SCOPUS:70249088033

SN - 3642020283

SN - 9783642020285

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 127

EP - 133

BT - Graph Theory, Computational Intelligence and Thought - Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday

A2 - Lipshteyn, Marina

A2 - Levit, Vadim E.

A2 - McConnell, Ross M.

ER -