## Abstract

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(m3^{2}^{n3}) algorithm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality. Assume that a weight function w is defined on the edges of G. Then G is w-equimatchable if all its maximal matchings are of the same weight. For every graph G, the set of weight functions w such that G is w-equimatchable is a vector space. We present an O(m·^{n4}+^{n5}logn) algorithm, which receives an input graph G, and outputs the vector space of weight functions w such that G is w-equimatchable.

Original language | English |
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Pages (from-to) | 99-106 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 338 |

Issue number | 3 |

DOIs | |

State | Published - 6 Mar 2015 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2014 Elsevier B.V.

## Keywords

- Claw-free graph
- Equimatchable graph
- Maximal independent set
- Maximal matching
- Well-covered graph