New Construction Techniques for \(H_{2}(8t, 3)s\)

An \( H_2 \) graph is a multigraph on three vertices with a double edge between one pair of distinct vertices and a single edge between the other two pairs. The problem of decomposing a complete multigraph \( 3K_{8t} \) into \( H_2 \) graphs has been completely solved. In this paper, we describe some new procedures for such decompositions and pose the following question: Can these procedures be adapted or extended to provide a unified proof of the existence of \( H_2(8t, \lambda) \)’s?