2-perfect m-cycle systems
نویسندگان
چکیده
منابع مشابه
Completing some spectra for 2-perfect cycle systems
The determination of the spectrum for the decomposition of Kv into 2-perfect m-cycle systems is completed here for several small values of m. In particular, the cases m = 9, 12 and 16 are completed (except for three isolated cases). Other isolated 2-perfect m-cycle systems, some listed as unknown in a recent survey paper by Lindner and Rodger, have been found: namely, for Kv where (m,v) = (7,21...
متن کاملNon - Isomorphic 2 - Perfect 6 - Cycle Systems of Order 13
It is known that necessary and sufficient conditions for the existence of a 2-perfect 6-cycle system of order n are that n = 1 or 9 mod 12 and n > 9 (Lindner, Phelps and Rodger [2]). Hence the smallest possible order of such a system is 13. The existence of a 2-perfect 6-cycle system of order 13 is shown by example in [2]. The example is cyclic. It is obvious that for large n the construction o...
متن کاملCorrigendum: The spectrum for 3-perfect 9-cycle systems
In [1], Theorem 1.1 should include the case v = 9; that is, it should say: THEOREM 1.1 The necessary and sufficient conditions for a 3-perfect 9-cycle decomposition of Kv are v == 1 or 9 (mod 18). However, the existence of this cycle system does not simplify the constructions used in the rest of the paper.
متن کاملThe spectrum for 3-perfect 9-cycle systems
A decomposition of Kn into 3-perfect 9-cycles is shown to exist if and only if n == 1 or 9 (modulo 18), n =1= 9.
متن کامل2-perfect Closed M-trail Systems of the Complete Directed Graph with Loops
Certain decompositions of complete directed graphs with loops into collections of closed trails which partition the edge set of the graph give rise to, and arise from, quasigroups. Such decompositions are said to be 2-perfect. The existence of these 2-perfect decompositions in which the closed trails are all of the same length m is examined. In particular, the set of values of n for which the o...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90626-q