Equitable path decomposition of graphs

Abstract

A decomposition of a graph is a collection of its edge — disjoint subgraphs whose union equals the edge set of the graph. A decomposition all of whose members are paths is called a path decomposition. In this paper, we introduce and initiate a study of a new variation of decomposition namely equitable path decomposition of a graph [Formula: see text] which is defined to be a decomposition in which all the members are paths and the lengths of any two paths are differ by at most one in [Formula: see text]. In this paper, we initiate a study on this parameter.