# Well-covered graphs and extendability

- Authors
- Journal
- Discrete Mathematics 0012-365X
- Publisher
- Elsevier
- Publication Date
- Volume
- 126
- Identifiers
- DOI: 10.1016/0012-365x(94)90253-4
- Disciplines

## Abstract

Abstract A graph is k-extendable if every independent set of size k is contained in a maximum independent set. This generalizes the concept of a B-graph (i.e. 1-extendable graph) introduced by Berge and the concept of a well-covered graph (i.e. k-extendable for every integer k) introduced by Plummer. For various graph families we present some characterizations of well-covered and k-extendable graphs. We show that in order to determine whether a graph is well-covered it is sometimes sufficient to verify that it is k-extendable for small values of k. For many classes of graphs, this leads to efficient algorithms for recognizing well-covered graphs.

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