Linear Time Recognition of P4-Indifferent Graphs - Rizzi, Romeo (BRICS Report Series, 1999)
A simple graph is P4-indifferent if it admits a total order < on its nodes such that every chordless path with nodes a, b, c, d and edges ab, bc, cd has a < b < c < d or a > b > c > d. P4-indifferent graphs generalize indifferent graphs and are perfectly orderable. Recently, Hoang, Maray and Noy gave a characterization of P4-indifferent graphs in terms of forbidden induced subgraphs. We clarify their proof and describe a linear time algorithm to recognize P4-indifferent graphs. When the input is a P4-indifferent graph, then the algorithm computes an order < as above. Key words: P4-indifference, linear time, recognition, modular decomposition.