an:05158396
Zbl 1291.05078
Araujo-Pardo, Gabriela; Olsen, Mika
Infinite families of \((n+1)\)-dichromatic vertex critical circulant tournaments
EN
Hliněný, Petr (ed.) et al., 6th Czech-Slovak international symposium on combinatorics, graph theory, algorithms and applications, DIMATIA Center, Charles University, Prague, Czech Republic, July 10--16, 2006. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 28, 141-144 (2007).
2007
a
05C20 05C15
digraph; circulant tournament; dichromatic number
Summary: In this talk we expose the results about infinite families of vertex critical \(r\)-dichromatic circulant tournaments for all \(r\geq 3\). The existence of these infinite families was conjectured by \textit{V. Neumann-Lara} [Discrete Math. 170, No. 1--3, 289--291 (1997; Zbl 0876.05039)], who later proved it for all \(r\geq 3\) and \(r\not= 7\). Using different methods we find explicit constructions of these infinite families for all \(r\geq 3\), including the case when \(r=7\), which complete the proof of the conjecture.
For the entire collection see [Zbl 1109.05007].
0876.05039