On graphs without a C 4 or a diamond

We consider the class of ( C 4 , diamond)-free graphs; graphs in this class do not contain a C 4 or a diamond as an induced subgraph. We provide an efficient recognition algorithm for this class. We count the number of maximal cliques in a ( C 4 , diamond)-free graph and the number of n -vertex, lab...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 159; no. 7; pp. 581 - 587
Main Authors Eschen, Elaine M., Hoàng, Chính T., Spinrad, Jeremy P., Sritharan, R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.04.2011
Subjects
[formula omitted]-free graphs
Diamond-free graphs
Recognition algorithm
Diamond-free graphs
C 4 -free graphs
Recognition algorithm
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Summary:We consider the class of ( C 4 , diamond)-free graphs; graphs in this class do not contain a C 4 or a diamond as an induced subgraph. We provide an efficient recognition algorithm for this class. We count the number of maximal cliques in a ( C 4 , diamond)-free graph and the number of n -vertex, labeled ( C 4 , diamond)-free graphs. We also give an efficient algorithm for finding a largest clique in the more general class of (house, diamond)-free graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2010.04.015