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Abstract: A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6` G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; ¯ C k 6` G). In this note we propose a new generalization of triangulated graphs. A graph G is slightly triangulated if it satisfies the two following conditions : 1. G contains no chordless cycle with at least 5 vertices. 2. For every induced subgraph H of G, there is a vertex in H the... (Update)
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BibTeX entry: (Update)
F. Maire, Slightly triangulated graphs are perfect, Graphs and Combin., 10 (1994) 263-268. http://citeseer.ist.psu.edu/maire95slightly.html More
@misc{ maire94slightly,
author = "F. Maire",
title = "Slightly triangulated graphs are perfect",
text = "F. Maire, Slightly triangulated graphs are perfect, Graphs and Combin.,
10 (1994) 263-268.",
year = "1994",
url = "citeseer.ist.psu.edu/maire95slightly.html" }
Citations (may not include all citations):488 Algorithmic Graph Theory and Perfect Graphs (context) - Golumbic - 1980
38 Perfect zero-one matrices (context) - Padberg - 1974
25 Optimizing weakly triangulated graphs (context) - Hayward, Hoang et al. - 1989
17 a property of the class of n-colorable graphs (context) - Seinsche - 1974
17 Graphical properties related to minimal imperfection (context) - Bland, Huang et al. - 1984
11 Perfectly Ordered Graphs (context) - Chv'atal - 1984
11 Topics on perfect graphs (context) - Berge, Chv'atal - 1984
10 strongly perfect graphs (context) - Berge, Duchet - 1984
9 Sur une conjecture relative au probleme des codes optimaux (context) - Berge - 1962
6 Combinatorial designs related to the perfect graph conjectur.. (context) - Chv'atal, Graham et al. - 1984
1 The graphs whose odd cycles have at leat two chords (context) - Meyniel - 1984
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