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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
Keywords:
tournament; oriented tree
Full Text:
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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