A LINEAR-TIME RECOGNITION ALGORITHM FOR P-4-REDUCIBLE GRAPHS

The P-4-reducible graphs are a natural generalization of the well-known class of cographs, with applications to scheduling, computational semantics, and clustering. More precisely, the P-4-reducible graphs are exactly the graphs none of whose vertices belong to more than one chordless path with three edges. A remarkable property of P-4-reducible graphs is their unique tree representation up to isomorphism. In this paper we present a linear-time algorithm to recognize P-4-reducible graphs and to construct their corresponding tree representation.