Covering Two-Edge-Coloured Complete Graphs with Two Disjoint Monochromatic Cycles
2008 ◽
Vol 17
(4)
◽
pp. 471-486
◽
Keyword(s):
In 1998 Łuczak Rödl and Szemerédi [7] 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.
Keyword(s):
Keyword(s):
Keyword(s):
2014 ◽
Vol 61
(1)
◽
pp. 51-78
◽
2002 ◽
Vol 50
(8)
◽
pp. 1935-1941
◽