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Covering two-edge-coloured complete graphs with two disjoint monochromatic cycles

Allen, Peter (2008) Covering two-edge-coloured complete graphs with two disjoint monochromatic cycles. Combinatorics, Probability and Computing, 17 (4). pp. 471-486. ISSN 0963-5483

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Identification Number: 10.1017/S0963548308009164

Abstract

In 1998 Łuczak Rödl and Szemerédi proved, by means of the Regularity Lemma, that there exists n0 such that, for any n ≥ n0 and two-edge-colouring of Kn, there exists a pair of vertex-disjoint monochromatic cycles of opposite colours covering the vertices of Kn. In this paper we make use of an alternative method of finding useful structure in a graph, leading to a proof of the same result with a much smaller value of n0. The proof gives a polynomial-time algorithm for finding the two cycles.

Item Type: Article
Official URL: http://journals.cambridge.org/action/displayJourna...
Additional Information: © 2008 Cambridge University Press
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 28 May 2012 14:58
Last Modified: 04 Jun 2014 13:02
URI: http://eprints.lse.ac.uk/id/eprint/44102

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