\(H\)–Equipackable Paths and Cycles for \(H = P_4\) and \(H = M_3\)

Abstract

A graph \(G\) is called \(H\)-equipackable if every maximal \(H\)-packing in \(G\) is also a maximum \(H\)-packing in \(G\). All \(M_2\)-equipackable graphs and \(P_3\)-equipackable graphs have been characterized. In this paper, \(P_k\)-equipackable paths, \(P_k\)-equipackable cycles, \(M_3\)-equipackable paths and \(M_3\)-equipackable cycles are characterized.