Graph connectivity | Graph families
In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected. (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
Vertex Cuts in Graphs (and a bit on Connectivity) | Graph Theory, Vertex-Connectivity
What is a vertex cut of a graph? And how can we use vertex cuts to describe how connected a graph is? We have discussed cut vertices and connected graphs before, but by tying them together in a way, we are able to characterize different levels of connectivity in graphs. The focus of this l
From playlist Graph Theory
Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
Vertex Connectivity of a Graph | Connectivity, K-connected Graphs, Graph Theory
What is vertex connectivity in graph theory? We'll be going over the definition of connectivity and some examples and related concepts in today's video graph theory lesson! The vertex connectivity of a graph is the minimum number of vertices you can delete to disconnect the graph or make
From playlist Graph Theory
Intro to Hypercube Graphs (n-cube or k-cube graphs) | Graph Theory, Hypercube Graph
What are hypercube graphs? Sometimes called n-cube or k-cube graphs, these graphs are very interesting! We’ll define hypercube graphs/k-cube graphs in today’s graph theory video lesson. We’ll also go over how to somewhat easily construct hypercube graphs, and some of their interesting prop
From playlist Graph Theory
Section 4b: Graph Connectivity
From playlist Graph Theory
Graph Theory: 53. Cut-Vertices
Here we introduce the term cut-vertex and show a few examples where we find the cut-vertices of graphs. We then go through a proof of a characterisation of cut-vertices: a vertex v is a cut-vertex if and only if there exist vertices u and w (distinct from v) such that v lies on every u-w
From playlist Graph Theory part-9
Discrete Math - 10.2.2 Special Types of Graphs
Introduction to cycles, wheels, complete graphs, hypercubes and bipartite graphs, including using the graph coloring technique to determine if a graph is bipartite. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII
From playlist Discrete Math I (Entire Course)
Edge Connectivity of Complete Graphs | Graph Theory
What is the edge connectivity of Kn, the complete graph on n vertices? In other words, what is the minimum number of edges we must delete to disconnect Kn? We'll prove this is n-1 in today's graph theory video lesson! For K1, the trivial graph, we define its edge connectivity to be 1. Fo
From playlist Graph Theory
Lecture 20 - Trees and Connectivity
This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Michal Pilipczuk: Introduction to parameterized algorithms and applications, lecture III
The mini-course will provide a gentle introduction to the area of parameterized complexity, with a particular focus on methods connected to (integer) linear programming. We will start with basic techniques for the design of parameterized algorithms, such as branching, color coding, kerneli
From playlist Summer School on modern directions in discrete optimization
Random k-out subgraphs - Or Zamir
Computer Science/Discrete Mathematics Seminar II Topic: Random k-out subgraphs Speaker: Or Zamir Affiliation: Member, School of Mathematics Date: March 09, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Proof: Complement of Regular Non-Eulerian Graph is Eulerian | Graph Theory, Euler Graphs
If the complement of a connected, regular, non-Eulerian graph is also connected, then it is Eulerian! We will prove this result in today's graph theory lesson using some argument about the degree sums of different graphs, and whether they're even or odd! Proof connected graph is Eulerian
From playlist Graph Theory
Proof: Menger's Theorem | Graph Theory, Connectivity
We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see
From playlist Graph Theory
Proof: Two Longest Paths Have a Common Vertex | Graph Theory, Connected Graphs
In any connected graph, two longest paths will always have a common vertex! We'll prove this theorem in today's video graph theory lesson using contradiction! We suppose we have two longest paths in a connected graph that do NOT have a common vertex, and we'll be able to find a longer pat
From playlist Graph Theory
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture introduces a single source shortest path algorithm that wor
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
A Classification of Planar Graphs - A Proof of Kuratowski's Theorem
A visually explained proof of Kuratowski's theorem, an interesting, important and useful result classifying "planar" graphs. Proof adapted from: http://math.uchicago.edu/~may/REU2017/REUPapers/Xu,Yifan.pdf and: https://www.math.cmu.edu/~mradclif/teaching/228F16/Kuratowski.pdf Also check
From playlist Summer of Math Exposition Youtube Videos
Simple Bounds on Vertex Connectivity | Graph Theory
We know that the vertex connectivity of a graph is the minimum number of vertices that can be deleted to disconnect it or make it trivial. We may then ask, what is an upper bound on the connectivity of a graph? What is a lower bound on the vertex connectivity of a graph? We give the most b
From playlist Graph Theory