Decomposition of a $2K_{10t+5}$ into $H_3$ Graphs

Abstract

An $H_3$ graph is a multigraph on three vertices with double edges between two pairs of distinct vertices and a single edge between the third pair. To settle the $H_3$ decomposition problem completely, one needs to complete the decomposition of a $2K_{10t+5}$ into $H_3$ graphs. In this paper, we present two new construction methods for such decompositions, resulting in previously unknown decompositions for $v=15,25,35,45$ and two new infinite families.