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1996•Journal of Graph TheoryRequires access

Minimal non-neighborhood-perfect graphs

Andr�s Gy�rf�s, Dieter Kratsch, Jenő Lehel, Frédéric Maffray

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Abstract

Neighborhood-perfect graphs form a subclass of the perfect graphs if the Strong Perfect Graph Conjecture of C. Berge is true. However, they are still not shown to be perfect. Here we propose the characterization of neighborhood-perfect graphs by studying minimal non-neighborhood-perfect graphs (MNNPG). After presenting some properties of MNNPGs, we show that the only MNNPGs with neighborhood independence number one are the 3-sun and 3K2. Also two further classes of neighborhood-perfect graphs are presented: line-graphs of bipartite graphs and a 3K2-free cographs. © 1996 John Wiley & Sons, Inc.

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What this paper is about

Neighborhood-perfect graphs form a subclass of the perfect graphs if the Strong Perfect Graph Conjecture of C. Berge is true. However, they are still not shown to be perfect. Here we propose the characterization of neighborhood-perfect graphs by studying minimal non-neighborhood-perfect graphs (MNNPG). After presenting some properties of MNNPGs, we show that the only MNNPGs with neighborhood independence number one are the 3-sun and 3K2. Also two further classes of neighborhood-perfect graphs are presented: line-graphs of bipartite graphs and a 3K2-free cographs. © 1996 John Wiley & Sons, Inc.

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Available abstract

Neighborhood-perfect graphs form a subclass of the perfect graphs if the Strong Perfect Graph Conjecture of C. Berge is true. However, they are still not shown to be perfect. Here we propose the characterization of neighborhood-perfect graphs by studying minimal non-neighborhood-perfect graphs (MNNPG). After presenting some properties of MNNPGs, we show that the only MNNPGs with neighborhood independence number one are the 3-sun and 3K2. Also two further classes of neighborhood-perfect graphs are presented: line-graphs of bipartite graphs and a 3K2-free cographs. © 1996 John Wiley & Sons, Inc.

Key concepts: Strong perfect graph theorem, Combinatorics, Mathematics, Trivially perfect graph, Cograph, Perfect graph theorem, Perfect graph, Chordal graph

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