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On the Alspach Conjecture

Published online by Cambridge University Press:  24 May 2001

P. N. BALISTER
P. N. BALISTER
Affiliation:
Department of Mathematical Sciences, University of Memphis, 3725 Norriswood, TN 38152, USA (e-mail: balistep@msci.memphis.edu)
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Abstract

It has been conjectured by Alspach [2] that given integers n and m1, …, mt with 3 [les ] mi [les ] n and [sum ]ti=1mi = (n2) (n odd) or [sum ]ti=1mi = (n2) − n/2 (n even), then one can pack Kn (n odd) or Kn minus a 1-factor (n even) with cycles of lengths m1, …, mt. In this paper we show that if the cycle lengths mi are bounded by some linear function of n and n is sufficiently large then this conjecture is true.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 2 , March 2001 , pp. 95 - 125
Copyright
2001 Cambridge University Press

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