Further results on almost resolvable cycle systems and the Hamilton-Waterloo problem
نویسندگان
چکیده
منابع مشابه
The directed almost resolvable Hamilton-Waterloo problem
In this paper, a result is proved that provides a general method of attack that can be used to solve the existence problem for partitions of the directed edges of Dn, the complete directed graph on n. vertices into r and n r almost parallel classes of directed cycles of length m1 and m2 respectively in the case where n\ and, ?rl2 &r€ €v€r. Use of this technique is then demonstrated by essential...
متن کاملExistence of almost resolvable directed 5-cycle systems
A directed k-cycle system of order n is a pair ( S, T ), where S is an n-set and T is a collection of arc disjoint directed k-cycles that partition the complete directed graph Kn *. An almost parallel class with deficiency x is a set of directed k-cycles which form a partition of S \ {x}. An almost resolvable directed k-cyclc system is a directed k-cyclc system in which the cycles can be partit...
متن کاملThe Hamilton-waterloo Problem for Two Even Cycles Factors
This paper investigates the problem of factoring K2n − In into 2-factors of two kinds or three kinds: (1) Ct-factors and C2t-factors, (2) C4-factors and C2t-factors, (3) C4-factors, C8-factors and C16-factors.
متن کاملOn α-resolvable directed cycle systems for cycle length 4
A directedm-cycle system of order v with index λ, denotedm-DCS(v, λ), is a collection of directed cycles of length m whose directed edges partition the directed edges of λDKv. An m-DCS(v, λ) is α-resolvable if its directed cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a des...
متن کاملFurther results on almost Moore digraphs
The nonexistence of digraphs with order equal to the Moore bound Md;k = 1+d+: : :+d k for d; k > 1 has lead to the study of the problem of the existence ofàlmost' Moore digraphs, namely digraphs with order close to the Moore bound. In 1], it was shown that almost Moore digraphs of order Md;k ? 1, degree d, diameter k (d; k 3) contain either no cycle of length k or exactly one such cycle. In thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2017
ISSN: 1063-8539
DOI: 10.1002/jcd.21571