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A Note on Vertex-Disjoint Cycles

Published online by Cambridge University Press:  14 February 2002

JACQUES VERSTRAËTE
JACQUES VERSTRAËTE
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, England (e-mail: jbav2@dpmms.cam.ac.uk)
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Abstract

Häggkvist and Scott asked whether one can find a quadratic function q(k) such that, if G is a graph of minimum degree at least q(k), then G contains vertex-disjoint cycles of k consecutive even lengths. In this paper, it is shown that if G is a graph of average degree at least k2+19k+10 with sufficiently many vertices, then G contains vertex-disjoint cycles of k consecutive even lengths, answering the above question in the affirmative. The coefficient of k2 cannot be decreased and, in this sense, this result is best possible.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 1 , January 2002 , pp. 97 - 102
Copyright
2002 Cambridge University Press

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