The support size of a factorization is the sum over the factors of the number of distinct edges in each factor. The spectrum of support sizes of \(l\lambda\)-factorizations of \(\lambda K_n\) and \(\lambda K_{n,n}\) are completely determined for all \(\lambda\) and \(n\).
Citation
S. Ajoodani-Namini. On The Factorizations of Complete Graphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 023. 183-196. .