Rizzi, Romeo (2001) *On the Recognition of P4-Indifferent Graphs.* UNSPECIFIED.

## 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, Hoang, 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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