We consider the class of (C4, diamond)-free graphs; graphs in this class do not contain a C4 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 (C4, diamond)-free graph and the number of n-vertex, labeled (C4, diamond)-free graphs. We also give an efficient algorithm for finding a largest clique in the more general class of (house, diamond)-free graphs.
@article{arxiv.0909.4719,
title = {On graphs without a C4 or a diamond},
author = {Elaine M. Eschen and Chinh T. Hoang and Jeremy P. Spinrad and R. Sritharan},
journal= {arXiv preprint arXiv:0909.4719},
year = {2009}
}