Abstract
S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a stable set of maximum size in the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S.
It is known that Ψ(G) is a greedoid for every forest G, [10]. Bipartite graphs and triangle-free graphs, whose families of local maximum stable sets form greedoids were characterized in [11] and [12], respectively.
The clique corona is the graph G = H ∘ {H 1,H 2,...,H n } obtained by joining each vertex v k of the graph H with the vertices of some clique H k , respectively. In this paper we demonstrate that if G is a clique corona, then Ψ(G) forms a greedoid on its vertex set.
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Levit, V.E., Mandrescu, E. (2008). The Clique Corona Operation and Greedoids. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_36
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DOI: https://doi.org/10.1007/978-3-540-85097-7_36
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