Geodesic
On Sets of Arcs Containing No Cycles in a Tournament*
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 261-264

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A tournament Tn with n nodes is a complete asymmetric digraph [2]. A set S of arcs of a tournament is called consistent if the tournament contains no oriented cycles composed entirely of arcs of S [1]. The object of this note is to provide a new lower bound for f(n), the greatest integer k such that every tournament with n nodes contains a set of k consistent arcs. Erdös and Moon [1] showed that where [x] denotes the largest integer not exceeding x, and the second inequality holds for any fixed ∈ > 0 and all sufficiently large n. 
Reid, K.B. On Sets of Arcs Containing No Cycles in a Tournament*. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 261-264. doi: 10.4153/CMB-1969-032-x
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     author = {Reid, K.B.},
     title = {On {Sets} of {Arcs} {Containing} {No} {Cycles} in a {Tournament*}},
     journal = {Canadian mathematical bulletin},
     pages = {261--264},
     year = {1969},
     volume = {12},
     number = {3},
     doi = {10.4153/CMB-1969-032-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-032-x/}
}
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