Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree

Abstract

We show that for every η > 0, there exists n 0 such that for every even n, n ≥ n 0 , and every graph G with (2 + η)n vertices and minimum degree at least (7/4 + 4η)n, each colouring of the edges of G with three colours results in a monochromatic cycle of length n.