Abstract
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 n 2 ( 1 + o ( 1 ) ) and there are tournaments for which f ( G ) > n 2 / 3000 . For general G we prove that f ( G ) ⩽ ⌊ n 2 / 3 ⌋ and this is tight. Some related parameters are also considered.
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