Colour-biased Hamilton cycles in random graphs

Abstract

We prove that a random graph $G(n,p)$, with $p$ above the Hamiltonicity threshold, is typically such that for any $r$-colouring of its edges there exists a Hamilton cycle with at least $(2/(r+1)-o(1))n$ edges of the same colour. This estimate is asymptotically optimal.

20 pages, minor corrections