Ramsey-Type Results for Unions of Comparability Graphs

Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand, there exist such graphs for which the largest clique and independent set are of size at most n0.4118 . Similar results are obtained for graphs which are a union of a fixed number k of comparability graphs. We also show that the same bounds hold for unions of perfect graphs. A geometric application is included.

• Type: Journal
• Year: 2002
• Where: GC
• Authors: Adrian Dumitrescu, Géza Tóth
• Keywords: Applied Computing, Clique, Comparability Graphs, GC 2002, Largest Clique