Basu, A.; Saha, P. K.; Sen, M. Further characterizations for interval tournaments. (English) Zbl 1247.05089 J. Indian Math. Soc., New Ser. 78, No. 1-4, 15-26 (2011). Summary: A tournament is a complete oriented graph and a tournament that is an interval digraph is an interval tournament. Interval tournaments have been characterized in terms of forbidden subtournaments. It has also been proved that a tournament with \(n\)-vertices is an interval tournament if and only if it has a transitive \((n-1)\)-subtournament. We provide here an alternative proof of these characterizations. Our approach helps us to obtain other characterizations of interval tournaments. One of these characterizations is that a tournament is an interval tournament if and only if all of its 3-cycles have a common vertex. We then obtain another characterization in terms of three forbidden subdigraphs. Lastly we characterize the complement of an interval tournament in terms of two-clique circular-arc graphs. MSC: 05C20 Directed graphs (digraphs), tournaments 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C75 Structural characterization of families of graphs Keywords:complete oriented graph; interval tournament; interval digraph; forbidden subtournaments; transitive subtournaments; 3-cycles; common vertex; forbidden subdigrpahs; two-clique circular arc-graphs PDFBibTeX XMLCite \textit{A. Basu} et al., J. Indian Math. Soc., New Ser. 78, No. 1--4, 15--26 (2011; Zbl 1247.05089)