The maximum number of Hamiltonian paths in tournaments

Abstract

Solving an old conjecture of Szele we show that the maximum number of directed Hamiltonian paths in a tournament onn vertices is at mostc · n 3/2 · n!/2n−1, wherec is a positive constant independent ofn.

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Research supported in part by a U.S.A.-Israel BSF grant and by a Bergmann Memorial Grant.

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Alon, N. The maximum number of Hamiltonian paths in tournaments. Combinatorica 10, 319–324 (1990). https://doi.org/10.1007/BF02128667

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 35
  • 05 C 38