Abstract
Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of Hi, where . Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph has a -decomposition if and only if k is even, and .
Highlights
Shyu [12] investigated the problem of decomposing Kn into paths and stars with k edges, giving a necessary and sufficient condition for k = 3
In [13], Shyu considered the existence of a decomposition of Kn into paths and cycles with k edges, giving a necessary and sufficient condition for k = 4
Shyu [14] investigated the problem of decomposing Kn into cycles and stars with k edges, settling the case k = 4
Summary
Balanced Complete Bipartite Multigraph, Cycle, Path, Star, Decomposition A G-decomposition of F is a partition of the edge set of F into copies of G. Shyu [12] investigated the problem of decomposing Kn into paths and stars with k edges, giving a necessary and sufficient condition for k = 3 .
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