Optimally ranking unrankable tournaments

@article{Spencer1980OptimallyRU,
  title={Optimally ranking unrankable tournaments},
  author={Joel H. Spencer},
  journal={Periodica Mathematica Hungarica},
  year={1980},
  volume={11},
  pages={131-144}
}
  • J. Spencer
  • Published 1 June 1980
  • Economics
  • Periodica Mathematica Hungarica

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References

SHOWING 1-4 OF 4 REFERENCES

Optimal ranking of tournaments

Let us be given a tournament Tn (i-e., a complete directed graph) on n players. It is natural to look for a ranking (linear order) L on the n players that best reflects the tournament result.

Probabilistic Methods in Combinatorics

In 1947 Paul Erdős [8] began what is now called the probabilistic method. He showed that if \(\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right){{2}^{{1 - \left( {\begin{array}{*{20}{c}}

On Sets of Consistent Arcs in a Tournament

A (round-robin) tournament Tn consists n of nodes u1, u2, …, un such that each pair of distinct nodes ui and uj is joined by one of the (oriented) arcs or The arcs in some set S are said to be