Kn(?) is fully {P7, S4}-decomposable

Abstract

Let Pk+1 denote a path of length k, Sm denote a star with m edges, and Kn(?) denote the complete multigraph on n vertices in which every pair of distinct vertices is joined by ? edges. In this paper, we have obtained the necessary conditions for a {Pk+1, Sm}-decomposition of Kn(?) and proved that the necessary conditions are also sufficient when k = 6 and m = 4.