CDAM: Computational, Discrete and Applicable Mathematics@LSE

CDAM Research Report, LSE-CDAM-2007-18

July 2007

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

Peter Allen

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 K_n, there exists a pair of vertex disjoint monochromatic cycles of opposite colours covering the vertices of K_n. 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.

A PDF file (172 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2007-18, together with your name and postal address to:

CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.

Phone: +44(0)-20-7955 7494.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk

		Introduction to the CDAM Research Report Series.
		CDAM@LSE Homepage.

		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk