Graph theory objects | Graph minor theory
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges. The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the complete bipartite graph K3,3. The Robertson–Seymour theorem implies that an analogous forbidden minor characterization exists for every property of graphs that is preserved by deletions and edge contractions.For every fixed graph H, it is possible to test whether H is a minor of an input graph G in polynomial time; together with the forbidden minor characterization this implies that every graph property preserved by deletions and contractions may be recognized in polynomial time. Other results and conjectures involving graph minors include the graph structure theorem, according to which the graphs that do not have H as a minor may be formed by gluing together simpler pieces, and Hadwiger's conjecture relating the inability to color a graph to the existence of a large complete graph as a minor of it. Important variants of graph minors include the topological minors and immersion minors. (Wikipedia).
Edge Cuts and Edge Connectivity | Graph Theory
Edge cuts, minimum edge cuts, minimal edge cuts, and edge connectivity are all introduced in today's graph theory lesson! Edge cuts are similar to vertex cuts but, of course, with edges! An edge cut of a nontrivial graph G is a set, X, of edges of G, such that G-X is disconnected. The car
From playlist Graph Theory
A subgraph consist of nodes and edges of a larger graph. In this tutorial I show you what a subgraph is and present an elegant representation in Mathematica. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale an
From playlist Introducing graph theory
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: 62. Graph Minors and Wagner's Theorem
In this video, we begin with a visualisation of an edge contraction and discuss the fact that an edge contraction may be thought of as resulting in a multigraph or simple graph, depending on the application. We then state the definition a contraction of edge e in a graph G resulting in a
From playlist Graph Theory part-10
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
A formal definition of a Graph and its properties
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: 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
Kevin Hendrey - Obstructions to bounded branch-depth in matroids (CMSA Combinatorics Seminar)
Kevin Hendrey (Institute for Basic Science) presents “Obstructions to bounded branch-depth in matroids”, 24 November 2020 (CMSA Combinatorics Seminar).
From playlist CMSA Combinatorics Seminar
Victor-Emmanuel Brunel: Learning Determinantal point processes from moments and cycles
Recording during the "Meeting in Mathematical Statistics" the December 21, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Ahmad Abdi: Packing odd T-joins with at most two terminals
Ahmad Abdi: Packing odd T-joins with at most two terminals Let T be an even vertex subset, of size at most two, and let S be an edge subset of a graph. An edge subset is odd if it contains an odd number of edges of S. We are interested in packing edge-disjoint odd T-joins. The maximum siz
From playlist HIM Lectures 2015
Bojan Mohar: Embedding extension problems
Recording during the thematic meeting: "Graphs and surfaces: algorithms, combinatorics and topology" the May 12, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematici
From playlist Mathematical Aspects of Computer Science
Writing Equations of Ellipses In Standard Form and Graphing Ellipses - Conic Sections
This algebra video tutorial explains how to write the equation of an ellipse in standard form as well as how to graph the ellipse when in standard form. It explains how to find the coordinates of the foci, vertices, and co-vertices. This video contains plenty of examples and practice pr
From playlist New Calculus Video Playlist
Ramsey classes and sparsity for finite models - J. Nešetřil - Workshop 1 - CEB T1 2018
Jaroslav Nešetřil (Prague) / 31.01.2018 In the talk we relate two notions in the title particularly in the context of sparse dense dichotomy (nowhere and somewhere dense classes and stability) and Ramsey classes of finite models in the context of the characterisation programme. A joint wo
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
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
Graphs as geometric objects - Nathan Linial
Computer Science/Discrete Mathematics Seminar I Topic: Graphs as geometric objects Speaker: Nathan Linial Affiliation: The Hebrew University Date: July 25, 2022 It may seem quite obvious that graphs carry a lot of geometric structure. Don't we learn in algorithm classes how to solve all
From playlist Mathematics
This video is about tournaments and some of their basic properties.
From playlist Basics: Graph Theory
Graph Theory: Basic Definitions
This video describes some basic definitions associated with graph theory.
From playlist Basics: Graph Theory
Ex 2: Graph an Ellipse with Center at the Origin and Vertical Major Axis
This video provides an example of how to graph the standard equation of an ellipse with the center at the origin and a horizontal major axis. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Graphing and Writing Equations of Ellipses