P4-Comparability Graphs

In 1981, Chvátal defined the class of perfectly orderable graphs. This class of perfect graphs contains the comparability graphs. In this paper, we introduce a new class of perfectly orderable graphs, the P4-comparability graphs. This class generalizes comparability graphs in a natural way. We also prove a decomposition theorem which leads to a structural characterization of P4-comparability graphs. Using this characterization, we develop a polynomial-time recognition algorithm and polynomial-time algorithms for the clique and colouring problems for P4-comparability graphs.