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Largest digraphs contained in alln-tournaments

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Abstract

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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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science Hebrew University, 91904, Jerusalem, Israel

    N. Linial

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, N. J., USA

    M. Saks

  3. Department of Analysis I., Eötvös University, H-1088, Budapest, Hungary

    Vera T. Sós

Authors
  1. N. Linial
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  2. M. Saks
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  3. Vera T. Sós
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Additional information

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). https://doi.org/10.1007/BF02579345

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  • DOI: https://doi.org/10.1007/BF02579345

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