On the Recognition of Probe Graphs of Some Self-Complementary Classes of Perfect Graphs

Abstract

In this paper we consider the recognition of some probe graph classes. Given a class of graphs \(\mathcal{G}\), a graph G is a probe graph of \(\mathcal{G}\) if its vertices can be partitioned into a set ℙ of probes and an independent set ℕ of nonprobes, such that G can be extended to a graph of \(\mathcal{G}\) by adding edges between certain nonprobes. We show that there are polynomial-time recognition algorithms for probe cographs, probe P4-reducible graphs, probe P4-sparse graphs, and probe splitgraphs.