## Abstract

A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a linear set function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same weight. The set of weight functions w for which a graph is w-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is w-well-covered can be done in polynomial time, if the input graph contains neither C_{4} nor C_{5} nor C_{6} nor C_{7}.

Original language | English |
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Pages (from-to) | 354-359 |

Number of pages | 6 |

Journal | Discrete Applied Mathematics |

Volume | 159 |

Issue number | 5 |

DOIs | |

State | Published - 6 Mar 2011 |

Externally published | Yes |

## Keywords

- Generating subgraph
- Hereditary system
- Independent set
- Relating edge
- Well-covered graph

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