an:05687581
Zbl 1185.05071
Araujo-Pardo, Gabriela; Olsen, Mika
A conjecture of Neumann-Lara on infinite families of \(r\)-dichromatic circulant tournaments
EN
Discrete Math. 310, No. 3, 489-492 (2010).
0012-365X
2010
j
05C20 05C15 05C63
circulant tournament; dichromatic number; vertex critical
Summary: We exhibit infinite families of vertex critical \(r\)-dichromatic circulant tournaments for all \(r \geq 3\). The existence of these infinite families was conjectured by Neumann-Lara [\textit{V. Neumann-Lara}, ``Vertex critical 4-dichromatic circulant tournaments'', Discrete Math. 170, No.\,1-3, 289--291 (1997; Zbl 0876.05039)], who later proved it for all \(r \geq 3\) and \(r \neq 7\). Using different methods, we provide new constructions of such infinite families for all \(r \geq 3\), which covers the case \(r = 7\) and thus settles the conjecture.
0876.05039