A tournament is a directed graph (digraph) obtained by assigning a direction for each edge in an undirected complete graph. That is, it is an orientation of a complete graph, or equivalently a directed graph in which every pair of distinct vertices is connected by a directed edge (often, called an arc) with any one of the two possible orientations. Many of the important properties of tournaments were first investigated by H. G. Landau in to model dominance relations in flocks of chickens. Current applications of tournaments include the study of voting theory and social choice theory among other things. The name tournament originates from such a graph's interpretation as the outcome of a round-robin tournament in which every player encounters every other player exactly once, and in which no draws occur. In the tournament digraph, the vertices correspond to the players. The edge between each pair of players is oriented from the winner to the loser. If player beats player , then it is said that dominates . If every player beats the same number of other players (indegree = outdegree), the tournament is called regular. (Wikipedia).
Intro to Tournament Graphs | Graph Theory
We introduce directed tournament graphs, which can be thought of as a graph representing the outcome of a round robin tournament - where vertices represent teams, and directed edges (arcs) go from winners to losers. We'll also discuss how many labelled tournaments there are on n vertices,
From playlist Graph Theory
This video is about tournaments and some of their basic properties.
From playlist Basics: Graph Theory
Transitive Tournaments (Directed Graphs) | Graph Theory
We introduce transitive tournaments and look at some neat properties they possess! Recall a tournament graph is a directed graph with exactly one arc between each pair of vertices. In other words, it is an orientation of a complete graph. #GraphTheory We say a tournament T is transitive i
From playlist Graph Theory
Proof for Distances from Tournament's Maximum Outdegree Vertex | Graph Theory
We prove that a vertex of maximum outdegree in a tournament has a distance less than or equal to 2 to every vertex in the graph. The proof is pretty straightforward, and mostly just takes advantage of the definition of a tournament and what maximum outdegree means. Recall a tournament is a
From playlist Graph Theory
Proof: Every Tournament has Hamiltonian Path | Graph Theory
We prove that every tournament graph contains a Hamiltonian path, that is a path containing every vertex of the graph. Recall a tournament is a directed graph with exactly one arc between each pair of vertices. The proof will proceed by contradiction, and follow a similar format to other p
From playlist Graph Theory
Graph Theory: 02. Definition of a Graph
In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio
From playlist Graph Theory part-1
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph Theory
Proof: Tournament is Transitive iff it has No Cycles | Graph Theory
We prove that a tournament graph is transitive if and only if it has no cycles. Recall a tournament is a directed graph with exactly one arc between each pair of vertices, and we say a tournament T is transitive if whenever (u,v), and (v,w) are arcs of T, (u,w) is an arc as well. We'll see
From playlist Graph Theory
Overview of algorithms in Graph Theory
An overview of the computer science algorithms in Graph Theory Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-theory-algorithms Previous video (intro): h
From playlist Graph Theory Playlist
Introduction to Natural Quasirandomness: Unique Colorability and Order-ability - Leonardo Coregliano
Computer Science/Discrete Mathematics Seminar II Topic: Introduction to Natural Quasirandomness: Unique Colorability and Orderability Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: November 08, 2022 The theory of graph quasirandomness studies sequences of g
From playlist Mathematics
Proof: Vertices of Strong Tournament Lie on Triangles | Graph Theory
We prove that every vertex of a strongly connected tournament graph lie on a triangle (a 3-cycle). #GraphTheory ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: http
From playlist Graph Theory
The absorption method, and an application to an old Ramsey problem - Matija Bucic
Computer Science/Discrete Mathematics Seminar II Topic: The absorption method, and an application to an old Ramsey problem Speaker: Matija Bucic Affiliation: Veblen Research Instructor, School of Mathematics Date: March 29, 2022 The absorption method is a very simple yet surprisingly pow
From playlist Mathematics
A glimpse of continuous combinatorics via natural quasirandomness - Leonardo Coregliano
Short Talks by Postdoctoral Members Topic: A glimpse of continuous combinatorics via natural quasirandomness Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: September 23, 2021
From playlist Mathematics
Graph Theory: 04. Families of Graphs
This video describes some important families of graph in Graph Theory, including Complete Graphs, Bipartite Graphs, Paths and Cycles. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https://www.youtube.com/watch?v=S1Zwhz-MhCs (Graph Theory: 02. Definit
From playlist Graph Theory part-1
Colouring Tournaments - Paul Seymour
Paul Seymour Princeton University December 13, 2010 A ``tournament'' is a digraph obtained from a complete graph by directing its edges, and ``colouring'' a tournament means partitioning its vertex set into acyclic subsets (``acyclic'' means the subdigraph induced on the subset has no dire
From playlist Mathematics