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Resolvable Mendelsohn triple systems with equal sized holes

✍ Scribed by F. E. Bennett; R. Wei; L. Zhu

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 165 KB
Volume: 5
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1997)5:5<329::aid-jcd2>3.0.co;2-h

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✦ Synopsis

An HMTS of type {n1 , n2 , . . . , n h } is a directed graph DKn 1 ,n 2 ,...,n h , which can be decomposed into 3-circuits. If the 3-circuits can be partitioned into parallel classes, then the HMTS is called an RHMTS. In this article it is shown that the RHMTSs of type m h exist when mh ≡ 0 (mod 3) and (m, h) / = (1, 6), with the possible exception of h = 6 and m / ∈ M17 , where M17 = {m|m is divisible by a prime less than 17}. The existence of Mendelsohn frames, which is closely related to RHMTS, is also considered in this article. It is proved that a Mendelsohn frame of type t u exists if and only if u ≥ 4 and t(u -1) ≡ 0 (mod 3) with 2 possible exceptions.

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