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Circulant tournaments of prime order are tight. (English) Zbl 1198.05083
Summary: We say that a tournament is tight if for every proper 3-coloring of its vertex set there is a directed cyclic triangle whose vertices have different colors. In this paper, we prove that all circulant tournaments with a prime number \(p\geq 3\) of vertices are tight using results relating to the acyclic disconnection of a digraph and theorems of additive number theory.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C05 Trees
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