Score Vectors and Tournaments with Cyclic Chromatic Number \(1\) or \(2\)

The cyclic chromatic number is the smallest number of colours needed to colour the nodes of a tournament so that no cyclic triple is monochromatic. Bagga, Beineke, and Harary \({[1]}\) conjectured that every tournament score vector belongs to a tournament with cyclic chromatic number \(1\) or \(2\). In this paper, we prove this conjecture and derive some other results.