Decomposition of $\lambda K_v$ into Multigraphs with Four Vertices and Five Edges

Abstract

We give necessary and sufficient conditions to decompose $\lambda$ copies, where necessarily $\lambda \ge 2$, of the complete graph $K_v$, into so-called “2-petal”, “stem-infinity”, “barbell”, and “box-edge” graphs, all with four vertices and five edges.