On the Hamilton-Waterloo problem

Adams, P, Billington, EJ, Bryant, DE and El-Zanati, SI (2002) On the Hamilton-Waterloo problem. Graphs And Combinatorics, 18 1: 31-51. doi:10.1007/s003730200001

Author Adams, P
Billington, EJ
Bryant, DE
El-Zanati, SI
Title On the Hamilton-Waterloo problem
Journal name Graphs And Combinatorics   Check publisher's open access policy
ISSN 0911-0119
Publication date 2002-01-01
Sub-type Article (original research)
DOI 10.1007/s003730200001
Volume 18
Issue 1
Start page 31
End page 51
Total pages 21
Editor J. Akiyama
Place of publication Japan
Publisher Springer-Verlag Tokyo
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.
Keyword Mathematics
Graph Decompositions
Graph Factorisations
Hamilton-waterloo Problem
Cycle Systems
Group-divisible Designs
Oberwolfach Problem
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Physical Sciences Publications
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Created: Wed, 15 Aug 2007, 03:06:37 EST