On the decomposition of λK into regular tournaments of order 5

✍ Scribed by A. Mahmoodi; R. Mathon

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 558 KB
• Volume: 2
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.3180020305

✦ Synopsis

Abstract

An RTD[5,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 RTD[5,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 B[5,2; v] which is not RT~5~‐directable. © 1994 John Wiley & Sons, Inc.