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Almost resolvable cycle systems—an analogue of Hanani triple systems

✍ Scribed by C. C. Lindner; M. Meszka; A. Rosa

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 123 KB
Volume: 17
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20204

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✦ Synopsis

Abstract

The purpose of this paper is the initiation of an attack on the general existence problem for almost resolvable 2__k__‐cycle systems. We give a complete solution for 2__k__=6 as well as a complete solution modulo one possible exception for 2__k__=10 and 14. We also show that the existence question for almost resolvable 2__k__‐cycle systems can be settled if we can show the existence for the two smallest possible orders 4__k__+1 and 8__k__+1. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 404–410, 2009

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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