Decomposition of a \(2K_{10t}\) into \(H_3\) graphs. (Q2828845)

A complete multigraph \(mK_n\) is the multigraph on \(n\) vertices where every pair of vertices is joined by exactly \(m\) edges. \(H_3\) is the multigraph on three vertices in which two pairs of vertices are joined by two edges each and the remaining pair is joined by a single edge. It can be also viewed as \(2K_3\) minus one edge.NEWLINENEWLINE The authors completely solve the problem of decomposition of \(2K_{10t}\) into \(H_3\) using labeling techniques and one-factorizations. They also point out that the complete solution of \(H_3\) decomposition problem requires solving the decomposition of \(2K_{10t+5}\) for which they have so far found only a partial solution. The partial solution has not yet been published.