An Application of Partitioned Balanced Tournament Designs to the Construction of Semiframes with Block Size Two

Abstract

We employ a well-known class of designs to give a complete solution to the problem of determining the spectrum of uniform semiframes with block size two. As a corollary we prove that the complete graph $K_{gu}$, admits a one-factorization with an orthogonal set of $u$ disjoint sub-one-factorizations of $K_g$ if and only if $g$ is even and $u\ge 3$.