On graphs without a C4 or a diamond

TL;DR

This paper studies (C4, diamond)-free graphs, providing recognition algorithms, counting maximal cliques, and extending to find largest cliques in (house, diamond)-free graphs, advancing understanding of these graph classes.

Contribution

It introduces efficient algorithms for recognizing (C4, diamond)-free graphs, counts maximal cliques, and extends to (house, diamond)-free graphs.

Findings

Efficient recognition algorithm for (C4, diamond)-free graphs

Counting of maximal cliques in these graphs

Algorithm for largest clique in (house, diamond)-free graphs

Abstract

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.