Decompositions of complete multigraphs derived from Hadamard matrices (Q1399905)

Let \(\mu K_v\) be the complete multigraph with \(v\geq 2\) vertices and \(\mu\) edges between each pair of vertices, and let \(b(\mu K_v)\) be the minimum number of complete bipartite subgraphs needed to partition the edge set of \(\mu K_v\). The authors determine the value of \(b(\mu K_v)\) for \(\mu\) odd and all \(v\leq 2\mu\), subject to the existence of certain Hadamard and conference matrices. Together with results by \textit{D. A. Gregory} and \textit{K. N. Vander Meulen} [J. Comb. Theory, Ser. A 82, 158-167 (1998; Zbl 0908.05071)], this completes the determination of \(b(\mu K_v)\) for all \(\mu\) and all \(v\leq 2\mu\).