Decompositions of complete multigraphs derived from Hadamard matrices

Let b(μKv) be the minimum number of complete bipartite subgraphs needed to partition the edge set of μKv, the complete multigraph with μ edges between each pair of vertices. Previous work by Gregory and Vander Meulen determined that for μ odd with v⩽2μ, and subject to the existence of certain Hadamard and conference matrices, then b(μKv) is one of two numbers. By considering forbidden submatrices of a vertex–biclique incidence matrix, we …