Abstract
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 P 4 -comparability graphs. This class generalizes comparability graphs in a natural way. We also prove a decomposition theorem which leads to a structural characterization of P 4 -comparability graphs. Using this characterization, we develop a polynomial-time recognition algorithm and polynomial-time algorithms for the clique and colouring problems for P 4 -comparability graphs.
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