A lower bound on the size of an absorbing set in an arc-coloured tournament

Abstract

Bousquet, Lochet and Thomassé recently gave an elegant proof that for any integer $n$, there is a least integer $f(n)$ such that any tournament whose arcs are coloured with $n$ colours contains a subset of vertices $S$ of size $f(n)$ with the property that any vertex not in $S$ admits a monochromatic path to some vertex of $S$. In this note we provide a lower bound on the value $f(n)$.