Decompositions of $\lambda K_n$ using Stanton-type Graphs

Abstract

A Stanton-type graph $S(n,m)$ is a connected multigraph on $n$ vertices such that for a fixed $m$ with $n-1\le m\le (\genfrac{}{}{0ex}{}{n}{2})$, there is exactly one edge of multiplicity $i$ (and no others) for each $i=1,2,\dots ,m$. In this note, we show how to decompose $\lambda K_n$ (for the appropriate minimal values of $\lambda$) into Stanton-type graphs $S(4,3)$ of the LOE and OLE types.