TY - JOUR

T1 - Graph operations that are good for greedoids

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

PY - 2010/7/6

Y1 - 2010/7/6

N2 - S is a local maximum stable set of a graph G, and we write S ε ψ, if the set S is a maximum stable set of the subgraph induced by S [N(S) , where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that ψ is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively. In this paper we give necessary and sufficient conditions for ψ to form a greedoid, where G is: (a) the disjoint union of a family of graphs; (b) the Zykov sum of a family of graphs; (c) the corona X o{H1; H2; ⋯ Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx.

AB - S is a local maximum stable set of a graph G, and we write S ε ψ, if the set S is a maximum stable set of the subgraph induced by S [N(S) , where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that ψ is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively. In this paper we give necessary and sufficient conditions for ψ to form a greedoid, where G is: (a) the disjoint union of a family of graphs; (b) the Zykov sum of a family of graphs; (c) the corona X o{H1; H2; ⋯ Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx.

KW - Corona

KW - Greedoid

KW - Local maximum stable set

KW - Zykov sum

UR - http://www.scopus.com/inward/record.url?scp=81955165108&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2010.04.009

DO - 10.1016/j.dam.2010.04.009

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AN - SCOPUS:81955165108

SN - 0166-218X

VL - 158

SP - 1418

EP - 1423

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 13

ER -