Minimal separators in -tidy graphs

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.