Decompositions of \(\lambda K_n\) into LOE and OLE Graphs

Abstract

Hein and Sarvate show how to decompose \(\lambda\) copies of a complete graph \(K_n\), for some minimal value of \(\lambda\), into so-called LOE and OLE graphs. In this paper, we will show that for all possible values of \(\lambda\), the necessary conditions are sufficient for the LOE and OLE decompositions.