A note on colour-bias Hamilton cycles in dense graphs

Abstract

Balogh, Csaba, Jing and Pluhár recently determined the minimum degree threshold that ensures a $2$-coloured graph $G$ contains a Hamilton cycle of significant colour bias (i.e., a Hamilton cycle that contains significantly more than half of its edges in one colour). In this short note we extend this result, determining the corresponding threshold for $r$-colourings.

6 pages, 2 figures. Author accepted manuscript, to appear in the SIAM Journal on Discrete Mathematics