### 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 - 1986 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

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

**Neighborhood perfect graphs.** / Lehel, J.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 61, no. 1, pp. 93-101. https://doi.org/10.1016/0012-365X(86)90031-2

}

TY - JOUR

T1 - Neighborhood perfect graphs

AU - Lehel, J.

AU - Tuza, Z.

PY - 1986

Y1 - 1986

N2 - The notion of neighborhood perfect graphs is introduced here as follows. Let G be a graph, αN(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′) = αN(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) = αN(G) is given for interval graphs.

AB - The notion of neighborhood perfect graphs is introduced here as follows. Let G be a graph, αN(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′) = αN(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) = αN(G) is given for interval graphs.

UR - http://www.scopus.com/inward/record.url?scp=38249040822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249040822&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(86)90031-2

DO - 10.1016/0012-365X(86)90031-2

M3 - Article

AN - SCOPUS:38249040822

VL - 61

SP - 93

EP - 101

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -