Abstract
A simple graph is P 4 -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. P 4-indifferent graphs generalize indifferent graphs and are perfectly orderable. Recently, Hoàng; Maffray and Noy gave a characterization of P 4-indifferent graphs in terms of forbidden induced subgraphs. We clarify their proof and describe a linear time algorithm to recognize P 4-indifferent graphs. When the input is a P 4-indifferent graph, then the algorithm computes an order < as above.
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