The spectrum for large sets of disjoint mendelsohn triple systems with any index

Abstract

Abstract The spectrum for LMTS( v ,1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS( v ,3). Furthermore, by the existence of LMTS( v ,1) and LMTS( v ,3), the spectrum for LMTS( v ,λ) is completed, that is v ≡ 2 (mod λ), v ≥ λ + 2, if λ ≢ 0(mod 3) then v ≢ 2 (mod 3) and if λ = 1 then v ≠ 6. © 1994 John Wiley & Sons, Inc.