On The Factorizations of Complete Graphs

S. Ajoodani-Namini1,2
1 Center for Theoretical Physics and Mathematics (AEOI) P.O. Box 11365-8486, Tehran, Iran
2Department of Mathematics 253-37 California Institute of Technology Pasadena, CA 91125, USA

Abstract

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 \(n\).