Remarks on hamiltonian digraphs

An oriented graph is an out-tournament if the out-neighbourhood of every vertex is a tournament. This note is motivated by A. Kemnitz and B. Greger, Gongr. Numer. 130 (1998) 127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-tournaments by Bang-Jensen, Huang and Prisner, J. Gombin. Theory Ser. B 59 (1993) 267-287. We also disprove a conjecture from the paper of Kemnitz and Greger.