ALGORITHMS ON SUBGRAPH OVERLAP GRAPHS

Abstract

Consider a graph D and a family FI of connected edge subgraphs of D. Let GI(V, F) be the intersection graph of FI and G the overlap graph of FI. We describe polynomial time algorithms for subgraph overlap graphs G when their intersection graphs GI have specific hereditary properties. The algorithms are to find maximum induced complete bipartite subgraphs, maximum weight holes of a given parity, minimum dominating holes, antiholes of a given parity and some others. In addition, we define the family of subgraph filament graphs based on D, FI and GI, and prove it to be the same as the family of subgraph overlap graphs.