The generalized almost resolvable cycle system problem

Adams, Peter, Billington, Elizabeth J., Hoffman, D. G. and Lindner, C. C. (2010) The generalized almost resolvable cycle system problem. Combinatorica, 30 6: 617-625. doi:10.1007/s00493-010-2525-z


Author Adams, Peter
Billington, Elizabeth J.
Hoffman, D. G.
Lindner, C. C.
Title The generalized almost resolvable cycle system problem
Journal name Combinatorica   Check publisher's open access policy
ISSN 0209-9683
1439-6912
Publication date 2010-11-01
Sub-type Article (original research)
DOI 10.1007/s00493-010-2525-z
Open Access Status Not yet assessed
Volume 30
Issue 6
Start page 617
End page 625
Total pages 9
Editor Alexander Schrijver
Laszlo Babai
Laszlo Lovasz
Place of publication Heidelberg, Germany
Publisher Springer
Language eng
Formatted abstract
Let (X, C) be a k-cycle system of order n, with vertex set X (of cardinality n) and collection of k-cycles C. Suppose n=kq+r where r < k. An almost parallel class of C is a collection of q=(n - r)/k pairwise vertex-disjoint k-cycles of C. Each almost parallel class thus will miss r of the n vertices in X. The k-cycle system (X, C) is said to be almost resolvable if C can be partitioned into almost parallel classes such that the remaining k-cycles are vertex disjoint. (These remaining k-cycles are referred to as a short parallel class.)

In this paper we (a) construct an almost resolvable 10-cycle system of every order congruent to 5 (mod 20), and (b) construct an almost resolvable 10-cycle system of order 41, thus completing the result that the spectrum for almost resolvable 10-cycle systems consists of all orders congruent to 1 or 5 (mod 20).
Keyword Hanani triple-systems
Oberwolfach problem
Length cycles
Decompositions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Created: Fri, 11 Feb 2011, 22:39:09 EST by Kay Mackie on behalf of !NON-HERDC