zbMATH — the first resource for mathematics

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 \(f(n)\leq(4+o(1))n\).

05C20 Directed graphs (digraphs), tournaments
05C35 Extremal problems in graph theory
05C05 Trees
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.