Independent set (graph theory)

Independent Vertex Sets | Graph Theory, Maximal and Maximum Independent Sets

What are independent vertex sets in graph theory? We'll go over independent sets, their definition and examples, and some related concepts in today's video graph theory lesson! A subset of the vertex set of a graph is an independent vertex set if and only if it contains no pair of adjace

From playlist Set Theory

Is the Empty Set an Independent Vertex Set? | Graph Theory Exercises

We prove the empty set is an independent set using the definition of independent vertex sets. We also show the empty set is an independent set by considering the complement of a vertex cover. Recall that an independent vertex set S of a graph G is a subset of the vertex set of G such that

From playlist Graph Theory Exercises

Complement of Independent Set is Vertex Cover | Graph Theory

We prove the complement of an independent vertex set is a vertex cover. This makes for an easy direct proof once we recall our definitions. An independent vertex set is a set of vertices, no two of which are adjacent. A vertex cover is a set of vertices such that every edge has at least on

From playlist Graph Theory

The Definition of a Graph (Graph Theory)

The Definition of a Graph (Graph Theory) mathispower4u.com

From playlist Graph Theory (Discrete Math)

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

Vertex Covers and Vertex Covering Numbers | Graph Theory

We introduce vertex covers, minimum vertex covers, and vertex covering numbers! We'll see some examples and non-examples of vertex covers, as well as minimum vertex covers and some that aren't minimum. The number of vertices in a minimum vertex cover is called the vertex covering number of

From playlist Graph Theory

Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o

From playlist Graph Theory FAQs

Vertex Covering Number of Complete Graphs | Graph Theory Exercises

We discuss and prove the vertex covering number of a complete graph Kn is n-1. That is, the minimum number of vertices needed to cover a complete graph is one less than its number of vertices. This is because, put simply, if we are missing at least 2 vertices in our attempted vertex cover,

From playlist Graph Theory Exercises

Complement of Vertex Cover is Independent Vertex Set | Graph Theory

We prove the complement of a vertex cover is an independent vertex set. Recall a vertex cover is a set of vertices covering all edges of the graph, meaning every edge has at least one end vertex in the cover. As a result, the complement of a cover cannot possible have two vertices joined b

From playlist Graph Theory

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

Matchings, Perfect Matchings, Maximum Matchings, and More! | Independent Edge Sets, Graph Theory

What are matchings, perfect matchings, complete matchings, maximal matchings, maximum matchings, and independent edge sets in graph theory? We'll be answering that great number of questions in today's graph theory video lesson! A matching in a graph is a set of edges with no common end-ve

From playlist Graph Theory

Graph Theory: 64. Vertex Colouring

In this video we define a (proper) vertex colouring of a graph and the chromatic number of a graph. We discuss some basic facts about the chromatic number as well as how a k-colouring partitions the vertex set into k independent sets (check out video #50 for more about independent sets).

From playlist Graph Theory part-11

Distributional symmetries and non commutative (...) - C. Male - Workshop 2 - CEB T3 2017

Camille Male / 26.10.17 Distributional symmetries and non commutative notions of independence The properties of the limiting non commutative distribution of random matrices can be usually understood thanks to the symmetry of the model, e.g. Voiculescu's asymptotic free independence occur

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Graph Theory: 50. Maximum vs Maximal

Here we describe the difference between two similar sounding words in mathematics: maximum and maximal. We use concepts in graph theory to highlight the difference. In particular, we define an independent set in a graph and a component in a graph and look at some examples. -- Bits of Gra

From playlist Graph Theory part-9

Graphs, vectors and integers - Noga Alon

Noga Alon Tel Aviv University; Visiting Professor, School of Mathematics December 1, 2014 The study of Cayley graphs of finite groups is related to the investigation of pseudo-random graphs and to problems in Combinatorial Number Theory, Geometry and Information Theory. I will discuss thi

From playlist Mathematics

More Graph Theory Definitions

This video explains the definitions of simple graphs, multigraphs, connected and not connected graphs, complete graphs, and the Handshake lemma. mathispower4u.com

From playlist Graph Theory (Discrete Math)