Minimal separators in P4-tidy graphs

We show that P4-tidy graphs have a linear number of minimal separators and present an algorithm to list them in linear time, extending an algorithm for P4-sparse graphs given by Nikolopoulos and Palios. We also give bounds on the number and total size of all minimal separators of P4-tidy and P4-lite graphs. Moreover, we show that these bounds are tight for such classes of graphs.