A counterexample to a conjecture on edge-coloured tournaments

We call the tournament T an m-coloured tournament if the arcs of T are coloured with m colours. In this paper we prove that for each n⩾6, there exists a 4-coloured tournament Tn of order n satisfying the two following conditions: (1) Tn does not contain C3 (the directed cycle of length 3, whose arcs are coloured with three distinct colours), and (2) Tn does not contain any vertex v such that for every other vertex x of Tn, there is a monochromatic directed path from x to v. This answers a question proposed by Shen Minggang in 1988.