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
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.
|Additional Information:||© 2008 Cambridge University Press|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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