Formulas In Connection With Parameters Related To Convexity Of Paths On Three Vertices: Caterpillars And Unit Interval Graphs

We present formulas to compute the P-3-interval number, the P-3-hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition, we find a connection between the percolation time of a unit interval graph and a parameter involving the diameter of a unit interval graph related to it. Finally, we present a hereditary graph class, defined by forbidden induced subgraphs, such that its percolation time is equal to one.