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 H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k...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 H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k</sub> and S<sub>k</sub> 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 .展开更多
文摘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 H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k</sub> and S<sub>k</sub> 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 .
