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

LUCÍA M. GONZÁLEZ; LUCIANO N. GRIPPO; MARTÍN D. SAFE

AUSTRALASIAN JOURNAL OF COMBINATORICS

Combinatorial Mathematics Society of Australasia

Año: 2021 vol. 79 p. 401 - 423

2202-3518

We present formulas to compute the P3 -interval number, the P3 -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.