On score sets for tournaments (Q1069952)

The score set of a tournament T consists of those integers s such that at least one node of T has score s. \textit{K. B. Reid} [Proc. 9th Southeast. Conf. on Combinatorics, graph theory, and computing, Boca Raton 1978, 607-618 (1978; Zbl 0414.05022)] conjectured that every set S of non- negative integers is the score set of some tournament T. The author proves this conjecture when S has four or five elements. [Remark: Yao Tianxing has recently announced a proof of Reids conjecture in general.]