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
Section 4b: Graph Connectivity
From playlist Graph Theory
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
Vertex Connectivity is Less than or Equal to Minimum Degree | Graph Theory Exercises
The vertex connectivity of every graph is less than or equal to its minimum degree, this is a simple upper bound on vertex connectivity. We prove this fact, and show an example, in today's graph theory video lesson. This inequality is true because if a graph G is disconnected, then its v
From playlist Graph Theory Exercises
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
Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► http
From playlist Geometry
Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► https
From playlist Geometry
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
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
Vertex Connectivity of the Petersen Graph | Graph Theory
What is the vertex connectivity of the Petersen graph? We'll go over the connectivity of this famous graph in today's graph theory video lesson. The vertex connectivity of the Petersen graph is 3. This means a minimum of 3 vertices can be deleted to disconnect it. We'll show this is true
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
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Proof: A Furthest Vertex is not a Cut Vertex | Graph Theory, Connected Graphs
Let u be a vertex of a connected and nontrivial graph G. Let v be a vertex of greatest distance from u in G. Then v is not a cut vertex of G. We prove this result in today's video graph theory lesson! This proof is a pretty straightforward contradiction proof. This result implies another
From playlist Graph Theory
Lecture 12 - Topological Sort & Connectivity
This is Lecture 12 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture16.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
What are Non-Separable Graphs? | Graph Theory
What are non-separable graphs? To understand non-separable graphs, we need to understand cut vertices. A vertex of a graph is a cut vertex if deleting it disconnects the graph or the component the vertex belongs to. Here is my lesson on cut vertices: https://www.youtube.com/watch?v=D1nYRg
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
This is a historical talk giving my recollections of how vertex algebras were discovered. It was requested by Michael Penn for his series of videos on vertex algebras https://www.youtube.com/playlist?list=PL22w63XsKjqyx2FFUywi_mz91Jtih52yX
From playlist Math talks