Largest digraphs contained in alln-tournaments


Letf(n) (resp.g(n)) be the largestm such that there is a digraph (resp. a spanning weakly connected digraph) onn-vertices andm edges which is a subgraph of every tournament onn-vertices. We prove that

$$n\log _2 n - c_1 n \geqq f(n) \geqq g(n) \geqq n\log _2 n - c_2 n\log \log n.$$

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Supported by the Chaim Weizman Postdoctoral Fellowship.

Supported in part by NSF under grant No. MCS-8102448.

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Linial, N., Saks, M. & Sós, V.T. Largest digraphs contained in alln-tournaments. Combinatorica 3, 101–104 (1983).

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 35
  • 05 C 55