On graphs without a C4 or a diamond

Authors:
Elaine M. Eschen;Chính T. Hoíng;Jeremy P. Spinrad;R. Sritharan
Affiliations:
Lane Department of Computer Science and Electrical Engineering, P.O. Box 6109, West Virginia University, Morgantown, WV 26506, United States;Department of Physics and Computing, Wilfrid Laurier University, Waterloo, Canada;Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235, United States;Computer Science Department, The University of Dayton, Dayton, OH 45469, United States
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

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.