Common multiples of paths and stars

Abstract

A graph G is a common multiple of two graphs H-1 and H-2 if G is both H-1-decomposable and H-2-decomposable. In this paper, we consider the case where H-1 is the path of length k Pk+1 and H-2 is the star with 1 edges S-1. We determine, for all positive integers k and 1, the set of integers q for which there exists a common multiple of Pk+1 and S-1 having precisely q edges.