Colour-biased Hamilton cycles in randomly perturbed graphs

Wenchong Chen, Xinbu Cheng, Zhifei Yan

Given a graph $G$ and an $r$-edge-colouring $\chi$ on $E(G)$, a Hamilton cycle $H\subset G$ is said to have $t$ colour-bias if $H$ contains $n/r+t$ edges of the same colour in $\chi$. Fr…