Decomposing oriented graphs into transitive tournaments

For an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is a tournament then f(G) < 5 21 n2 (1 + o(1)) and there are tournaments for which f(G) > n2 /3000. For general G we prove that f(G) n2 /3 and this is tight. Some related parameters are also considered. AMS classification code: 05C20, 05C70

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Raphael Yuster
• Keywords: DM 2006, Minimum Number, Oriented Graph, Transitive Subtournaments