Further results about large sets of disjoint Mendelsohn triple systems
نویسندگان
چکیده
Kang, Q. and Y. Chang, Further results about large sets of disjoint Mendelsohn triple systems, Discrete Mathematics 118 (I 993) 2633268. 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 distinct elements of X. The cyclic triple is denoted by (x, y, z) or ( y, z, x) or (z, x, y). A Mendelsohn triple system on X is a pair (X, B) where B is a collection of cyclic triples from X such that each ordered pair of distinct elements of X is covered by a unique cyclic triple from B. The system on X( [XI= v) is denoted by MTS(v). Mendelsohn [l] proved that the spectrum for MTS(u)s is the set of all v-0 or 1 (mod 3) and v#6. A large set of pairwise disjoint MTS(v)s is a collection of u2 pairwise disjoint MTS(v)s. It is denoted by LMTS(o). Up to now, all known results about LMTS(v) are: (Rl) There exists an LMTS(u) for v1,3 (mod 6) [2]; (R2) If there exists an LMTS(v), then there exists an LMTS(3n) [3]; (R3) If there exists an LMTS(V+ 1) and v>,3, then there exists an LMTS(~V+ 1) [3]; (R4) For p1 or 5 (mod 6), if there exists an LMTS(q +2), then there exists an LMTS(pq + 2) C2,41; Correspondence to: Qingde Kang, Mathematic Department, Hebei Normal College, Shijiazhuang 05009 I, Hebei, China. 0012-365X/93/$06.00
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عنوان ژورنال:
- Discrete Mathematics
دوره 118 شماره
صفحات -
تاریخ انتشار 1993