Related papers: Classifying Intrinsically Linked Tournaments by Sc…
A \emph{fair competition}, based on the concept of envy-freeness, is a non-eliminating competition where each contestant (team or individual player) may not play against all other contestants, but the total difficulty for each contestant is…
Let $a, \ b \ (b \geq a)$ and $n \ (n \geq 2)$ be nonnegative integers and let $\mathcal{T}(a,b,n)$ be the set of such generalised tournaments, in which every pair of distinct players is connected at most with $b$, and at least with $a$…
The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n-2 radar observations with the tracking rule "3 out of 5 with loss 2." This fact allows…
Given a tournament T=(V,A), a subset X of $V$ is an interval of T provided that for every a, b in X and x\in V-X, (a,x) in A if and only if (b,x) in A. For example, $\emptyset$, {x}(x in V) and V are intervals of T, called trivial…
We characterize the tournaments that are dominance graphs of sets of (unfair) coins in which each coin displays its larger side with greater probability. The class of these tournaments coincides with the class of tournaments whose vertices…
A diamond is a $4$-tournament which consists of a vertex dominating or dominated by a $3$-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of $n$-tournaments with the maximum number of diamonds…
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative…
A common form of competition is one where judges grade contestants' performances which are then compiled to determine the final ranking of the contestants. Unlike in another common form of competition where two contestants play a…
In this paper, we completely characterize the $m$-step competition graph of a bipartite tournament for any integer $m \ge 2$. In addition, we compute the competition index and the competition period of a bipartite tournament.
A directed graph $R^{\circ}$ on a set $X$ is a set of ordered pairs of distinct points called \emph{arcs}. It is a tournament when every pair of distinct points is connected by an arc in one direction or the other (and not both). We can…
A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a…
We prove that every $n$-vertex tournament has at most $n\left(\frac{n-1}{2}\right)^k$ walks of length $k$.
Given non-negative integers $n_{i}$ and $\alpha_{i}$ with $0 \leq \alpha_{i} \leq n_i$ $(i=1,2,...,k)$, an $[\alpha_{1},\alpha_{2},...,\alpha_{k}]$-$k$-partite hypertournament on $\sum_{1}^{k}n_{i}$ vertices is a $(k+1)$-tuple…
In this paper, we demonstrate a score based indexing approach for tennis videos. Given a broadcast tennis video (BTV), we index all the video segments with their scores to create a navigable and searchable match. Our approach temporally…
In 1981, Bermond and Thomassen conjectured that for any positive integer $k$, every digraph with minimum out-degree at least $2k-1$ admits $k$ vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture…
K\"uhn, Osthus, and Townsend asked whether there exists a constant $C$ such that every strongly $Ct$-connected tournament contains all possible $1$-factors with at most $t$ components. We answer this question in the affirmative. This is…
This paper is a survey of results and problems related to the following question: is it true that if G is a tournament with sufficiently large chromatic number, then G has two vertex-disjoint subtournaments A,B, both with large chromatic…
Document ranking experiments should be repeatable. However, the interaction between multi-threaded indexing and score ties during retrieval may yield non-deterministic rankings, making repeatability not as trivial as one might imagine. In…
Consider a randomly oriented graph $G=(V,E)$ and let $a$, $s$ and $b$ be three distinct vertices in $V$. We study the correlation between the events $\{a\to s\}$ and $\{s\to b\}$. We show that, when $G$ is the complete graph $K_n$, the…
Tournaments are orientations of the complete graph, and the directed Ramsey number $R(k)$ is the minimum number of vertices a tournament must have to be guaranteed to contain a transitive subtournament of size $k$, which we denote by…