%0 Journal Article
%T {C<sub>k</sub>, P<sub>k</sub>, S<sub>k</sub>} -Decompositions of Balanced Complete Bipartite Multigraphs
%A Jenq-Jong Lin
%A Min-Jen Jou
%J Open Journal of Discrete Mathematics
%P 174-179
%@ 2161-7643
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojdm.2016.63015
%X Let <img src=\"Edit_06a4ed5d-f1d8-47e9-951f-789740bf4e36.bmp\" alt=\"\" /> be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer <img src=\"Edit_60510a2f-43a0-4ad9-a71c-0c2286019235.bmp\" alt=\"\" />copies of H<sub>i</sub>, where <img src=\"Edit_2fda3525-66e1-4653-89d6-f0eb8df86da5.bmp\" alt=\"\" />. 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 <img src=\"Edit_7f7e25d2-014b-4558-9906-99344c4b51c4.bmp\" alt=\"\" />, we prove that a balanced complete bipartite multigraph <img src=\"Edit_f4ba538b-9488-4e28-93db-359eaf37bfea.bmp\" alt=\"\" />&nbsp;has a <img src=\"Edit_ca66ba7f-8d07-4587-90fd-5f8d8fb289a1.bmp\" alt=\"\" />-decomposition if and only if k is even, <img src=\"Edit_55cc6410-325a-4c95-a95d-aa1a03170904.bmp\" alt=\"\" />and <img src=\"Edit_f01cfe4e-edde-4c0e-93d3-9cc9463284a1.bmp\" alt=\"\" />.
%K Balanced Complete Bipartite Multigraph
%K Cycle
%K Path
%K Star
%K Decomposition
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=68338