Largest digraphs contained in alln-tournaments

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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References

  1. [1]

    B. Alspach andM. Rosenfeld, Realization of certain generalized paths in tournaments,Discr. Math. 34 199–202.

  2. [2]

    P. Erdős andL. Moser, On the representation of directed graphs as unions of orderings,Publ. Math. Inst. Hungar. Acad. Sci. 9 (1964), 125–132.

    Google Scholar 

  3. [3]

    R. Forcade, Parity of paths and circuits in tournaments,Discr. Math. 6 (1973), 115–118.

    MATH  Article  MathSciNet  Google Scholar 

  4. [4]

    B. Grünbaum, Antidirected Hamiltonian Paths in tournaments,J. Combinatorial Theory (B) 11 (1971), 249–257.

    MATH  Article  Google Scholar 

  5. [5]

    H. G. Landau, On dominance relations and the structure of animal societies, III; the condition for a score structure,Bull. Math. Biophys. 15 (1955), 143–148.

    Article  Google Scholar 

  6. [6]

    J. W. Moon,Topics on tournaments, Holt, Rinehart and Winston, New York, 1968.

    MATH  Google Scholar 

  7. [7]

    L. Rédei, Ein Kombinatorischer Satz,Acta Sci. Math. (Szeged) 7 (1934), 39–43.

    MATH  Google Scholar 

  8. [8]

    M. Rosenfeld, Antidirected Hamiltonian Circuits in tournaments,J. Combinatorial Theory (B) 16 (1974), 234–242.

    MATH  Article  MathSciNet  Google Scholar 

  9. [9]

    M. Saks andV. T. Sóss, On unavoidable subgraphs of tournaments, to appear.

Download references

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

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 35
  • 05 C 55