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 o {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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机译:S是G的局部最大稳定集,如果S是由S∪N(S)引起的子图中最大大小的稳定集,则我们写S∈Ψ(G),其中N(S)是G的邻域。 S.已知对于每个森林G,G(G)都是一个贪婪的物种[10]。二分图和无三角形图分别由[11]和[12]表征,它们的局部最大稳定集族形成了贪婪。集团电晕是通过将图H的每个顶点v_k与某个集团H_k的顶点分别连接而获得的图G = H o {H_1,H_2,...,H_n}。在本文中,我们证明了,如果G是集团电晕,则Ψ(G)在其顶点集上会形成一个贪婪。
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