相关论文: Structure of singular and nonsingular tournament m…
In this paper we introduce a new technique to analyze families of rankings focused on the study of structural properties of a new type of graphs. Given a finite number of elements and a family of rankings of those elements, we say that two…
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…
Motivated by his work on the classification of countable homogeneous oriented graphs, Cherlin asked about the typical structure of oriented graphs (i) without a transitive triangle, or (ii) without an oriented triangle. We give an answer to…
Decomposing a digraph into subdigraphs with a fixed structure or property is a classical problem in graph theory and a useful tool in a number of applications of networks and communication. A digraph is strongly connected if it contains a…
Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that admit…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
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…
An $n$-tournament $T$ with vertex set $V$ is simple if there is no subset $M$ of $V$ such that $2\leq \left \vert M\right \vert \leq n-1$ and for every $x\in V\setminus M$, either $M\rightarrow x$ or $x \rightarrow M$. The simplicity index…
The incomplete round robin sports tournament format, where each team plays the same number of games but faces only a subset of the other teams, is becoming increasingly popular in both youth and professional competitions. In contrast to…
A vertex $x$ in a tournament $T$ is called a king if for every vertex $y$ of $T$ there is a directed path from $x$ to $y$ of length at most 2. It is not hard to show that every vertex of maximum out-degree in a tournament is a king.…
The study of mutual visibility has traditionally focused on undirected graphs, asking for the maximum number of vertices that can communicate via shortest paths without intermediate interference from other set members. In this paper, we…
A monograph on the theory of tournament design focusing on brackets and multibrackets in particular.
To a given nonsingular triangular matrix A with entries from a ring, we associate a weighted bipartite graph G(A) and give a combinatorial description of the inverse of A by employing paths in G(A). Under a certain condition, nonsingular…
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…
Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…
The orientation completion problem for a class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class by orienting the unoriented edges of the partially oriented graph.…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
Tournaments are a widely used mechanism to rank alternatives in a noisy environment. This paper investigates a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the…