Formulas in connection with parameters related to convexity of paths on three vertices : caterpillars and unit interval graphs

Abstract

We present formulas to compute the P3-interval number, the P3-hullnumber and the percolation time for a caterpillar, in terms of certainsequences associated with it. In addition, we find a connection betweenthe percolation time of a unit interval graph and a parameter involvingthe diameter of a unit interval graph related to it. Finally, we presenta hereditary graph class, defined by forbidden induced subgraphs, suchthat its percolation time is equal to one.