# 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

### Spectral Slater index of tournaments

• Mathematics
The Electronic Journal of Linear Algebra
• 2022
The Slater index $i(T)$ of a tournament $T$ is the minimum number of arcs that must be reversed to make $T$ transitive. In this paper, we define a parameter $\Lambda(T)$ from the spectrum of the

### Extremal results on feedback arc sets in digraphs

• Mathematics
ArXiv
• 2022
. A directed graph is oriented if it can be obtained by orienting the edges of a simple, undirected graph. For an oriented graph G , let β ( G ) denote the size of a minimum feedback arc set , a

### On Explicit Random-Like Tournaments

A new construction of tournaments satisfying the quasi-random property based on digraph spectra and a digraph-version of the expander-mixing lemma is given and an application to the proof of the NP-hardness of the feedback arc set problem for tournaments is discussed.

### Dominant tournament families

For a tournament $H$ with $h$ vertices, its typical density is $h!2^{-\binom{h}{2}}/aut(H)$, i.e. this is the expected density of $H$ in a random tournament. A family ${\mathcal F}$ of $h$-vertex

### The Number of Tournaments with the Minimum Number of Upsets

• Mathematics
Graphs Comb.
• 2020
A construction method is provided which generates all tournament matrices with a prescribed score-list with minimum number of upsets by using bounds for the permanents of Ferrers matrices.

### Color Coding, Multilinear Detection, and Randomized Divide and Conquer

• Computer Science
• 2013
The important technique of color coding is introduced and the running times for randomized algorithms with Koutis’ idea of using algebraic general methods of speeding up algorithms obtained by color coding are shown.

## 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}}

• Mathematics