Bipartite graphs | Trees (graph theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence or out-tree—or making all its edges point towards the root—in which case it is called an anti-arborescence or in-tree. A rooted tree itself has been defined by some authors as a directed graph. A rooted forest is a disjoint union of rooted trees. A rooted forest may be directed, called a directed rooted forest, either making all its edges point away from the root in each rooted tree—in which case it is called a branching or out-forest—or making all its edges point towards the root in each rooted tree—in which case it is called an anti-branching or in-forest. The term "tree" was coined in 1857 by the British mathematician Arthur Cayley. (Wikipedia).
Graph Theory: 36. Definition of a Tree
In this video I define a tree and a forest in graph theory. I discuss the difference between labelled trees and non-isomorphic trees. I also show why every tree must have at least two leaves. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/zxu0dL436gI
From playlist Graph Theory part-7
Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions
What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree
From playlist Graph Theory
Graph Theory 37. Which Graphs are Trees
A proof that a graph of order n is a tree if and only if it is has no cycle and has n-1 edges. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/QFQlxtz7f6g - Graph Theory: 36. Definition of a Tree http://youtu.be/Yon2ndGQU5s - Graph Theory: 38. Three
From playlist Graph Theory part-7
Graph Theory: 38. Three ways to Identify Trees
A proof that a graph of order n is a tree if and only if it is connected and has n-1 edges. This, together with the previous video and the definition of a tree, gives three ways to determine if a graph is a tree. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http:/
From playlist Graph Theory part-7
Graph Theory: 39. Types of Trees
In this video we cover examples of types of trees that are often encountered in graph theory. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: 36. Definition of a Tree - https://www.youtube.com/watch?v=QFQlxtz7f6g 37. Which Graphs are Trees - https://ww
From playlist Graph Theory part-7
Introduction to Trees and Properties of Trees
This video introduces defines and gives the properties of tree graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
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
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
Tree Graphs - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
An introduction to the field of Graph Theory, the study of networks Algorithms repository: https://github.com/williamfiset/algorithms#graph-theory Slides: https://github.com/williamfiset/Algorithms/tree/master/slides/graphtheory Graph Theory Videos: https://www.youtube.com/playlist?list
From playlist Graph Theory Playlist
Diameter and Radius of Tree Graphs | Graph Theory
We discuss what family of tree graphs have maximum diameter, minimum diameter, maximum radius, and minimum radius. Recall the diameter of a graph is the maximum distance between any two vertices. The radius of a graph is the minimum eccentricity of any vertex. We'll find the star graphs ha
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
Graph Theory: 46. Relation Between Minimun Degree and Subtrees
It is not surprising that a tree of order k is a subgraph of a complete graph of order at least k. Here I'll explain the result that shows for every tree T of order k, any graph with minimum degree at least k-1 will contain a subgraph isomorphic to T. The proof is by induction on the ord
From playlist Graph Theory part-8
Natasha Dobrinen: Borel sets of Rado graphs are Ramsey
The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint fr
From playlist Combinatorics
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogu
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Proof: Tree Graphs Have at Least Two End Vertices | Graph Theory
Nontrivial tree graphs have at least two end vertices, sometimes called leaves, and we prove that graph theory result in today's video graph theory lesson! Remember a tree is a connected acyclic graph, which means connected with no cycles. And end vertices are vertices of degree one - ver
From playlist Graph Theory
This video introduces rooted trees and how to define the relationships among vertices in a rooted tree. mathispower4u.com
From playlist Graph Theory (Discrete Math)