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Trees in tournaments. (English) Zbl 0736.05041
Let \(f(n)\) denote the least integer \(N\) such that every tournament with \(N\) nodes contains every oriented tree with \(n\) nodes. The authors show that \(f(n)\leq 12n\) and \(f(n)\leq(4+o(1))n\).

MSC:
05C20 Directed graphs (digraphs), tournaments
05C35 Extremal problems in graph theory
05C05 Trees
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References:
[1] K. B. Reid, andN. C. Wormald: Embedding orientedn-trees in tournaments,Studia Sci. Math. Hungar. 18 (1983), 377-387. · Zbl 0489.05026
[2] A. G. Thomason: Paths and cycles in tournaments,Trans. Amer. Math. Soc. 296 (1986), 167-180. · Zbl 0599.05026 · doi:10.1090/S0002-9947-1986-0837805-6
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