Related papers: Counting Various Classes of Tournament Score Seque…
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…
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…
This article concerns the resolution of impartial combinatorial games, and in particular games that can be split in sums of independent positions. We prove that in order to compute the outcome of a sum of independent positions, it is always…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
We investigate tournaments with a specified score vector having additional structure: loopy tournaments in which loops are allowed, Hankel tournaments which are tournaments symmetric about the Hankel diagonal (the anti-diagonal), and…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tournament went given your scores? We determine the exact…
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…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to…
We introduce the notion of clique number of a tournament and investigate its relation with the dichromatic number. In particular, it permits defining $\dic$-bounded classes of tournaments, which is the paper's main topic.
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency…
We determine the inducibility of all tournaments with at most $4$ vertices together with the extremal constructions. The $4$-vertex tournament containing an oriented $C_3$ and one source vertex has a particularly interesting extremal…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Reid conjectured that any finite set of non-negative integers is the score set of some tournament and Yao gave a non-constructive proof of Reid's conjecture using arithmetic arguments. No constructive proof has been found since. In this…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal…