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A graph G is a common multiple of two graphs H₁ and H₂ if there exists a decomposition of G into edge-disjoint copies of H₁ and also a decomposition of G into edge-disjoint copies of H₂. If G is a common multiple of H₁ and H₂, and G has q edges, then we call G a (q, H₁, H₂) graph. Our paper deals with the following question: Given two graphs H₁ and H₂, for which values of q does there exist a (q, H₁, H₂) graph? when H₁ is either a path or a star with 3 or 4 edges and H₂ is a crown.
C. et al. (Wed,) studied this question.