Graph operations that are good for greedoids

AbstractS is a local maximum stable set of a graph G, and we write S∈Ψ(G), 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(G) 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(G) 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∘{H1,H2,…,Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx