Neighborhood perfect graphs

J. Lehel, Z. Tuza

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)93-101
Number of pages9
JournalDiscrete Mathematics
Volume61
Issue number1
DOIs
Publication statusPublished - 1986

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Perfect Graphs
Subgraph
Interval Graphs
Chordal Graphs
Induced Subgraph
Cover
Denote
Closed
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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

In: Discrete Mathematics, Vol. 61, No. 1, 1986, p. 93-101.

Research output: Contribution to journalArticle

Lehel, J. ; Tuza, Z. / Neighborhood perfect graphs. In: Discrete Mathematics. 1986 ; Vol. 61, No. 1. pp. 93-101.
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