| Abstract: | Let θ be a family of graphs. By a θ-decomposition of a graph G we mean a partition λ of the edge set of G such that every F ? π spans in G a subgraph isomorphic to a graph in θ. In this paper we state the following conjecture: If T1 and T2 are two trees having relatively prime sizes then there exists c = c(T1 T2) such that every graph G satisfying the condition δ(G) ? c has a {T1, T2}-decom-position. We prove this conjecture for some special pairs of trees. In particular, we prove it in the following cases: (i) T1 and T2 are stars having relatively prime sizes; (ii) T1 and T2 are paths having relatively prime sizes; and. (iii) T1 = T2 - {v}, where v is a terminal vertex in T 2. |
