%0 Journal Article
%T Monochromatic cycles and the monochromatic circumference in 2-coloured graphs
%A Alex Scott
%A Matthew White
%J Mathematics
%D 2011
%I arXiv
%X Li, Nikiforov and Schelp conjectured that a 2-edge coloured graph G with order n and minimal degree strictly greater than 3n/4 contains a monochromatic cycle of length l, for all l at least four and at most n/2. We prove this conjecture for sufficiently large n and also find all 2-edge coloured graphs with minimal degree equal to 3n/4 that do not contain all such cycles. Finally we show that, for all positive constants d and sufficiently large n, a 2-edge coloured graph G of order n with minimal degree at least 3n/4 either contains a monochromatic cycle of length at least (2/3+d/2)n, or, in one of the two colours, contains a cycle of all lengths between three and (2/3-d)n.
%U http://arxiv.org/abs/1107.5177v1