In graph theory, a k-outerplanar graph is a planar graph that has a planar embedding in which the vertices belong to at most concentric layers. The outerplanarity index of a planar graph is the minimum value of for which it is -outerplanar. (Wikipedia).
What are Planar Graphs? | Graph Theory
What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t
From playlist Graph Theory
Diameter and Radius of Tree Graphs | Graph Theory
We discuss what family of tree graphs have maximum diameter, minimum diameter, maximum radius, and minimum radius. Recall the diameter of a graph is the maximum distance between any two vertices. The radius of a graph is the minimum eccentricity of any vertex. We'll find the star graphs ha
From playlist Graph Theory
Determining if a set of points is a rhombus, square or rectangle
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Using a set of points determine if the figure is a parallelogram using the midpoint formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
How to determine if points are a rhombus, square or rectangle
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points is a parallelogram using the distance formula
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Edge Colorings and Chromatic Index of Graphs | Graph Theory
We introduce edge colorings of graphs and the edge chromatic number of graphs, also called the chromatic index. We'll talk about k-colorings/k-edge colorings, minimum edge colorings, edge colourings as matchings, edge colourings as functions, and see examples and non-examples of edge color
From playlist Graph Theory
Determining if a set of points makes a parallelogram or not
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
How to determine the perimeter of a quadrilateral using distance formula of four points
๐ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Proof: Necessary Component Condition for Graphs with Hamiltonian Paths | Graph Theory
Let G be a graph with a Hamiltonian path (a path containing all vertices of the graph). Then, if we delete any k vertices of G, the resulting graph will have at most k+1 components. We prove this result in today's video graph theory lesson! This is a fairly straightforward proof by induct
From playlist Graph Theory
Lower bounds for subgraph isomorphism โ Benjamin Rossman โ ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.3 Lower bounds for subgraph isomorphism Benjamin Rossman Abstract: We consider the problem of determining whether an ErdลsโRรฉnyi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of consta
From playlist Mathematical Aspects of Computer Science
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
Graph Theory: 46. Relation Between Minimun Degree and Subtrees
It is not surprising that a tree of order k is a subgraph of a complete graph of order at least k. Here I'll explain the result that shows for every tree T of order k, any graph with minimum degree at least k-1 will contain a subgraph isomorphic to T. The proof is by induction on the ord
From playlist Graph Theory part-8
Proof: Necessary Component Condition for Hamiltonian Graphs | Graph Theory
Let G be a Hamiltonian graph. Then deleting any k vertices from G results in a graph with at most k components. We prove this necessary component condition for Hamiltonian graphs in today's video graph theory lesson! Remember a Hamiltonian graph is a graph containing a Hamiltonian cycle -
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
Basic Absolute Value Function Translations: y=|x-h|+k
This video introduces translations of the absolute value function http://mathispower4u.com
From playlist Graphing and Finding Equations of Transformed Absolute Value Functions
Nexus Trimester - Andrew McGregor (University of Massachusetts) 2/2
New Algorithmic Techniques for Massives graphs - 2/2 Andrew McGregor (University of Massachusetts) March 15, 2016 Abstract: We'll present a 3 hour tutorial covering recent algorithmic results on processing massive graphs via random linear projections, aka sketches, and data streams.
From playlist 2016-T1 - Nexus of Information and Computation Theory - CEB Trimester
Random Cayley Graphs - Noga Alon
Noga Alon Tel Aviv University; Member, School of Mathematics November 25, 2013 The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the
From playlist Mathematics
Graph Theory: 59. Maximal Planar Graphs
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges. -- Bits of Graph Theory by Dr. Sarada Herke. Related videos: GT57 Planar G
From playlist Graph Theory part-10
Michal๔ฐ 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