W2-graphs and shedding vertices

@article{Levit2017W2graphsAS,
  title={W2-graphs and shedding vertices},
  author={Vadim E. Levit and Eugen Mandrescu},
  journal={Electronic Notes in Discrete Mathematics},
  year={2017},
  volume={61},
  pages={797-803}
}
A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A well-covered graph is 1-well-covered if the deletion of every vertex leaves a graph which is well-covered as well (Staples, 1975). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. It turns out that G ∈ W2 if and only if it is a 1-well… CONTINUE READING
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