Graph operations that are good for greedoids

Vadim E. Levit, Eugen Mandrescu

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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.

Original languageEnglish
Pages (from-to)1418-1423
Number of pages6
JournalDiscrete Applied Mathematics
Issue number13
StatePublished - 6 Jul 2010


  • Corona
  • Greedoid
  • Local maximum stable set
  • Zykov sum


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