On the decomposition of λK into regular tournaments of order 5

An RTD5,λ; v] is a decomposition of the complete symmetric directed multigraph, denoted by λK, into regular tournaments of order 5. In this article we show that an RTD5,λ; v] exists if and only if (v?1)λ ≡ 0 (mod 2) and v(v?1)λ ≡ 0 (mod 10), except for the impossible case (v,λ) = (15,1). Furthermore, we show that for each v ≡ 1,5 (mod 20), v ≠ 5, there exists a B5,2; v] which is not RT₅-directable. © 1994 John Wiley & Sons, Inc.