Computational problems in graph theory | NP-complete problems
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others. Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see .Two common examples of graph partitioning are minimum cut and maximum cut problems. (Wikipedia).
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Graph Neural Networks, Session 2: Graph Definition
Types of Graphs Common data structures for storing graphs
From playlist Graph Neural Networks (Hands-on)
This video is about tournaments and some of their basic properties.
From playlist Basics: Graph Theory
Section 4b: Graph Connectivity
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
Graph Theory FAQs: 04. Isomorphism vs Homomorphism
In this video we recall the definition of a graph isomorphism and then give the definition of a graph homomorphism. Then we look at two examples of graph homomorphisms and discuss a special case that relates to graph colourings. -- Graph Theory FAQs by Dr. Sarada Herke. Related videos:
From playlist Graph Theory FAQs
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
Graph Theory: 09. Graph Isomorphisms
In this video I provide the definition of what it means for two graphs to be isomorphic. I illustrate this with two isomorphic graphs by giving an isomorphism between them, and conclude by discussing what it means for a mapping to be a bijection. An introduction to Graph Theory by Dr. Sar
From playlist Graph Theory part-2
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
A Tight Bound for Hypergraph Regularity - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar I Topic: A Tight Bound for Hypergraph Regularity Speaker: Guy Moshkovitz Affiliation: Harvard University Date: Febuary 27, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Lecture 7. Graph partitioning algorithms.
Network Science 2021 @ HSE http://www.leonidzhukov.net/hse/2021/networks/
From playlist Network Science, 2021
6. Szemerédi's graph regularity lemma I: statement and proof
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Szemerédi's graph regularity lemma is a powerful tool in
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Chromatic Number of Bipartite Graphs | Graph Theory
What is the chromatic number of bipartite graphs? If you remember the definition, you may immediately think the answer is 2! This is practically correct, though there is one other case we have to consider where the chromatic number is 1. We'll explain both possibilities in today's graph th
From playlist Graph Theory
A Regularity Lemma with Modifications - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar II Topic: A Regularity Lemma with Modifications Speaker: Guy Moshkovitz Affiliation: Member, School of Mathematics Date: January 29, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Networks: Part 4 - Oxford Mathematics 4th Year Student Lecture
Network Science provides generic tools to model and analyse systems in a broad range of disciplines, including biology, computer science and sociology. This course (we are showing the whole course over the next few weeks) aims at providing an introduction to this interdisciplinary field o
From playlist Oxford Mathematics Student Lectures - Networks
A stable arithmetic regularity lemma in finite (...) - C. Terry - Workshop 1 - CEB T1 2018
Caroline Terry (Maryland) / 01.02.2018 A stable arithmetic regularity lemma in finite-dimensional vector spaces over fields of prime order In this talk we present a stable version of the arithmetic regularity lemma for vector spaces over fields of prime order. The arithmetic regularity l
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
9. Szemerédi's graph regularity lemma IV: induced removal lemma
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains a strengthening of the graph regulari
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Karen Vogtmann - On the cohomological dimension of automorphism groups of RAAGs
The class of right-angled Artin groups (RAAGs) includes free groups and free abelian groups, Both of these have extremely interesting automorphism groups, which share some properties and not others. We are interested in automorphism groups of general RAAGs, and in particular
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
A Proof on Hamiltonian Complete Bipartite Graphs | Graph Theory, Hamiltonian Graphs
Which complete bipartite graphs are Hamiltonian? We'll prove the answer to that question in today's graph theory lesson! A little bit of messing around with complete bipartite graphs might present the answer to you. The complete bipartite graph Kmn (m vertices in one partite set and n ver
From playlist Graph Theory