CDAM: Computational, Discrete and Applicable
CDAM Research Report, LSE-CDAM-2007-18
Covering two-edge-coloured complete graphs with two disjoint monochromatic cycles
Peter AllenIn 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.
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