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Berge graphs with chordless cycles of bounded length
Author(s) -
Rusu Irena
Publication year - 1999
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199909)32:1<73::aid-jgt7>3.0.co;2-7
Subject(s) - combinatorics , mathematics , chordal graph , strong perfect graph theorem , complement (music) , indifference graph , pathwidth , cograph , discrete mathematics , graph , split graph , 1 planar graph , line graph , biochemistry , chemistry , complementation , gene , phenotype
A graph is called weakly triangulated if it contains no chordless cycle on five or more vertices (also called hole ) and no complement of such a cycle (also called antihole ). Equivalently, we can define weakly triangulated graphs as antihole‐free graphs whose induced cycles are isomorphic either to C 3 or to C 4 . The perfection of weakly triangulated graphs was proved by Hayward [Hayward, J Combin Theory B. 39 (1985), 200–208] and generated intense studies to efficiently solve, for these graphs, the classical NP‐complete problems that become polynomial on perfect graphs. If we replace, in the definition above, the C 4 by an arbitrary C p ( p even, at least equal to 6), we obtain new classes of graphs whose perfection is shown in this article. In fact, we prove a more general result: for any even integer p ≥ 6, the graphs whose cycles are isomorphic either to C 3 or to one of C p , C p +2 , …, C 2 p 6 are perfect. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 73–79, 1999