We show that for every η>0, there exists n0 such that for every even n, n≥n0, 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.
@article{arxiv.2001.00643,
title = {Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree},
author = {Tomasz Łuczak and Zahra Rahimi},
journal= {arXiv preprint arXiv:2001.00643},
year = {2020}
}