In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three. By Vizing's theorem, the number of colors needed to edge color a simple graph is either its maximum degree Δ or Δ+1. For some graphs, such as bipartite graphs and high-degree planar graphs, the number of colors is always Δ, and for multigraphs, the number of colors may be as large as 3Δ/2. There are polynomial time algorithms that construct optimal colorings of bipartite graphs, and colorings of non-bipartite simple graphs that use at most Δ+1 colors; however, the general problem of finding an optimal edge coloring is NP-hard and the fastest known algorithms for it take exponential time. Many variations of the edge-coloring problem, in which an assignments of colors to edges must satisfy other conditions than non-adjacency, have been studied. Edge colorings have applications in scheduling problems and in frequency assignment for fiber optic networks. (Wikipedia).
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
Edge Coloring and the Chromatic Index of a Graph
This video introduces edge coloring and the chromatic index of a graph. An application of the chromatic index is provided. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Microsoft Edge: Customizing Edge
In this video, you’ll learn more about customizing Edge. Visit https://www.gcflearnfree.org/edge/customizing-edge/1/ for our text-based lesson. This video includes information on: • Choosing a homepage • Setting Edge as the default browser • Installing and removing extensions We hope you
From playlist Microsoft Edge
Microsoft Edge: Privacy and Security in Edge
In this video, you’ll learn more about privacy and security in Edge. Visit https://www.gcflearnfree.org/edge/privacy-and-security-in-edge/1/ for our text-based lesson. This video includes information on: • Maintaining privacy in Edge • Clearing browsing history and data • Creating a priva
From playlist Microsoft Edge
Microsoft Edge: Browsing in Edge
In this video, you’ll learn more about browsing in Edge. Visit https://www.gcflearnfree.org/edge/browsing-in-edge/1/ for our text-based lesson. This video includes information on: • Using windows and tabs • Viewing browsing history • Downloading and accessing files We hope you enjoy!
From playlist Microsoft Edge
Angle Side Relationships in a Triangle - Geometry
This video focuses on the angle side relationships in a triangle. In particular, I show students how to use the idea that the smallest angle is opposite the smallest side. This concept is used to order the sides of the triangle from least to greatest. Your feedback and requests are encour
From playlist Geometry
Beginning Graphic Design: Color
In this video, you’ll learn the basics of using color in graphic design. Visit https://www.gcflearnfree.org/beginning-graphic-design/color/1/ for our text-based lesson. This video includes information on: • Hue, saturation, and value • Creating monochromatic, analogous, and other color sc
From playlist Graphic Design
Determine the values of two angles that lie on a lie with a third angle
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
definition of adjacent angles
From playlist Common Core Standards - 8th Grade
8ECM Invited Lecture: Daniela Kühn
From playlist 8ECM Invited Lectures
Kernels, marriages, and the Dinitz problem #SoME2
The Dinitz problem is a graph theory problem proposed by Jeff Dinitz in 1979, and solved by Fred Galvin in 1994, 15 years later! In the video, I share the solution, along with some motivation that could have resulted in the solution. I hope you enjoy! I first heard of the problem in Diest
From playlist Summer of Math Exposition 2 videos
Hermann Weyl Lectures Topic: The PCP theorem Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor, School of Mathematics Date: November 18, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
Lecture 12 - Topological Sort & Connectivity
This is Lecture 12 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2007. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/2007/lecture12.pdf More informa
From playlist CSE373 - Analysis of Algorithms - 2007 SBU
Dieter Rautenbach: Restricted types of matchings
Abstract: We present new results concerning restricted types of matchings such as uniquely restricted matchings and acyclic matchings, and we also consider the corresponding edge coloring notions. Our focus lies on bounds, exact and approximative algorithms. Furthermore, we discuss some ma
From playlist Combinatorics
Louis Esperet: Coloring graphs on surfaces
Recording during the thematic meeting: "Graphs and surfaces: algorithms, combinatorics and topology" the May 11, 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
Lecture 12 - Depth-First Search
This is Lecture 12 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture12.pdf More inf
From playlist CSE373 - Analysis of Algorithms 2016 SBU
Angle Properties - Circle Geometry (Angles in the same segment)
More resources available at www.misterwootube.com
From playlist Circle Geometry