Minimal separators in $P_4$-tidy graphs

Abstract

We show that $P_4$-tidy graphs have a linear number of minimal separators and present an algorithm to list them in linear time, extending an algorithm for $P_4$-sparse graphs given by Nikolopoulos and Palios. We also give bounds on the number and total size of all minimal separators of $P_4$-tidy and $P_4$-lite graphs. Moreover, we show that these bounds are tight for such classes of graphs.