Related papers: Forcing Quasirandomness in a Regular Tournament

Chung, Graham, and Wilson proved that a graph is quasirandom if and only if there is a large gap between its first and second largest eigenvalue. Recently, the authors extended this characterization to k-uniform hypergraphs, but only for…

In 1982 Thomassen asked whether there exists an integer f(k,t) such that every strongly f(k,t)-connected tournament T admits a partition of its vertex set into t vertex classes V_1,...,V_t such that for all i the subtournament T[V_i]…

Real world tournaments are almost always intransitive. Recent works have noted that parametric models which assume $d$ dimensional node representations can effectively model intransitive tournaments. However, nothing is known about the…

We study the problem of scheduling asynchronous round-robin tournaments. We consider three measures of a schedule that concern the quality and fairness of a tournament. We show that the schedule generated by the well-known "circle design"…

Let a_1,...,a_k satisfy a_1+...+a_k=1 and suppose a k-uniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting…

A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…

Given a positive integer $m$, the $m$-step competition graph of a digraph $D$, denoted by $C^m(D)$, has the same vertex set as $D$ and has an edge between vertices $u$ and $v$ if and only if there exists a vertex $w$ such that there exist…

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…

We study the problem of extending partial isomorphisms for hypertournaments, which are relational structures generalizing tournaments. This is a generalized version of an old question of Herwig and Lascar. We show that the generalized…

We prove that isomorphism of tournaments of twin width at most $k$ can be decided in time $k^{O(\log k)}n^{O(1)}$. This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in…

We consider a game played on an initially empty graph where two players alternate drawing an edge between vertices subject to the condition that no degree can exceed $k$. We show that for $k=3$, either player can avoid a Hamilton cycle, and…

The traveling tournament problem is a well-known benchmark problem of the sports scheduling. We propose an approximation algorithm for the traveling tournament problem with the constraints such that both the number of consecutive home games…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations,…

The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such that any $n$-vertex tournament contains a copy of $H$ as a subgraph. We prove that the $1$-subdivision of the $k$-vertex transitive…

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on…

Moser asked for a construction of explicit tournaments on $n$ vertices having at least $(\frac{n}{3e})^n$ Hamilton cycles. We show that he could have asked for rather more.

We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…

Given a tournament $T$, a module of $T$ is a subset $M$ of $V(T)$ such that for $x, y\in M$ and $v\in V(T)\setminus M$, $(x,v)\in A(T)$ if and only if $(y,v)\in A(T)$. The trivial modules of $T$ are $\emptyset$, $\{u\}$ $(u\in V(T))$ and…

A directed graph where there is exactly one edge between every pair of vertices is called a {\em tournament}. Finding the "best" set of vertices of a tournament is a well studied problem in social choice theory. A {\em tournament solution}…