Balanced star decompositions of regular multigraphs and λ-fold complete bipartite graphs

Let S-k denote the star with k edges. A balanced S-k-decomposition of a multigraph G is a family D of subgraphs of G whose edge sets form a partition of the edge set of G such that each member of D is isomorphic to Sk, and every vertex of G belongs to the same number of members in D. In this paper, we obtain the following results: (1) A necessary and sufficient condition for an r-regular multigraph to have a balanced S-k-decomposition. (2) A necessary and sufficient condition for the lambda-fold complete bipartite graph lambda K-m.n to have a balanced Sk-decomposition. (c) 2005 Elsevier B.V. All rights reserved.