### Abstract

The notion of neighborhood perfect graphs is introduced here as follows. Let G be a graph, α_{N}(G) denote the maximum number of edges such that no two of them belong to the same subgraph of G induced by the (closed) neighborhood of some vertex; let ρ{variant}_{N}(G) be the minimum number of vertices whose neighborhood subgraph cover the edge set of G. Then G is called neighborhood perfect if ρ{variant}_{N}(G′) = α_{N}(G′) holds for every induced subgraph G′ of G. It is expected that neighborhood perfect graphs are perfect also in the sense of Berge. We characterized here those chordal graphs which are neighborhood perfect. In addition, an algorithm to computer ρ{variant}_{N}(G) = α_{N}(G) is given for interval graphs.

Original language | English |
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Pages (from-to) | 93-101 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 61 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1986 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Discrete Mathematics*,

*61*(1), 93-101. https://doi.org/10.1016/0012-365X(86)90031-2