On the Hamilton-Waterloo Problem |
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| Authors: | Peter Adams Elizabeth J Billington Darryn E Bryant Saad I El-Zanati |
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| Institution: | (1) Centre for Discrete Mathematics and Computing, Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072, Australia e-mail: ejb@maths.uq.edu.au, AU;(2) Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA, US |
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| 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
t
and the remaining s 2-factors consist of cycles of lengths b
1,b
2,…,b
u
(where necessarily ∑
i=1
t
a
i
=∑
j=1
u
b
j
=v). In this paper we consider the Hamilton-Waterloo problem in the case a
i
=m, 1≤i≤t and b
j
=n, 1≤j≤u. We obtain some general constructions, and apply these to obtain results for (m,n)∈{(4,6),(4,8),(4,16),(8,16),(3,5),(3,15),(5,15)}.
Received: July 5, 2000 |
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| Keywords: | , ,Graph decompositions, Graph factorisations, Hamilton-Waterloo problem, Cycle systems |
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