In this article it is shown that any resolvable Mendelsohn triple system of order u can be embedded in a resolvable Mendelsohn triple system of order v iff v 2 3u, except possibly for 71 values of (u,v). 0 1993 John Wiley & Sons, Inc. ## Theorem 1.1. A RMTS(v) exists if and only if If ( X , % ) a
New large sets of resolvable Mendelsohn triple systems
โ Scribed by Zhou, Junling; Chang, Yanxun
- Book ID
- 122209213
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 406 KB
- Volume
- 328
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
An MTS(v) [or DTS(v)] is said to be resolvable, denoted by RMTS(v) [or RDTS(v)], if its block set can be partitioned into parallel classes. An MTS(v) [or DTS(v)] is said to be almost resolvable, denoted by ARMTS(v) [or ARDTS(v)], if its bloak set can be partitioned into almost parallel classes. The
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 โก 0 (mod 3)
In this note, a construction of the large sets of pairwise disjoint Mendelsohn triple systems of order 72k + 6, where k > 1 and k F 1 or 2 (mod 3), is given. Let X be a set of v elements (v 2 3). A cyclic triple from X is a collection of three pairs (x, y), (y,z) and (z, x), where x,y and z are dis