Graph families

Well-covered graph

In graph theory, a well-covered graph is an undirected graph in which every minimal vertex cover has the same size as every other minimal vertex cover. Equivalently, these are the graphs in which all maximal independent sets have equal size. Well-covered graphs were defined and first studied by Michael D. Plummer in 1970. The well-covered graphs include all complete graphs, balanced complete bipartite graphs, and the rook's graphs whose vertices represent squares of a chessboard and edges represent moves of a chess rook. Known characterizations of the well-covered cubic graphs, well-covered claw-free graphs, and well-covered graphs of high girth allow these graphs to be recognized in polynomial time, but testing whether other kinds of graph are well-covered is a coNP-complete problem. (Wikipedia).

Well-covered graph
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Vertex Covering Number of Complete Graphs | Graph Theory Exercises

We discuss and prove the vertex covering number of a complete graph Kn is n-1. That is, the minimum number of vertices needed to cover a complete graph is one less than its number of vertices. This is because, put simply, if we are missing at least 2 vertices in our attempted vertex cover,

From playlist Graph Theory Exercises

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Vertex Covers and Vertex Covering Numbers | Graph Theory

We introduce vertex covers, minimum vertex covers, and vertex covering numbers! We'll see some examples and non-examples of vertex covers, as well as minimum vertex covers and some that aren't minimum. The number of vertices in a minimum vertex cover is called the vertex covering number of

From playlist Graph Theory

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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

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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

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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

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What is a Path Graph? | Graph Theory

What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can

From playlist Graph Theory

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The Definition of a Graph (Graph Theory)

The Definition of a Graph (Graph Theory) mathispower4u.com

From playlist Graph Theory (Discrete Math)

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Graph Neural Networks, Session 2: Graph Definition

Types of Graphs Common data structures for storing graphs

From playlist Graph Neural Networks (Hands-on)

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Features of Graphs, Domain, Range (Precalculus - College Algebra 7)

Support: https://www.patreon.com/ProfessorLeonard Cool Mathy Merch: https://professor-leonard.myshopify.com Finding Point, Domain, Range and other features of graphs of functions.

From playlist Precalculus - College Algebra/Trigonometry

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Dimers and Integrability - Richard Kenyon

Richard Kenyon Brown University March 29, 2013 This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integr

From playlist Mathematics

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Lecture 22 - More Reductions

This is Lecture 22 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/lecture24.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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NP Completeness III - More Reductions - Lecutre 17

All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c

From playlist ArsDigita Algorithms by Shai Simonson

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NP Completeness IV - Lecture 18

All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c

From playlist ArsDigita Algorithms by Shai Simonson

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Idealness of k-wise intersecting families, by Tony Huynh

CMSA Combinatorics Seminar, 6 October 2020

From playlist CMSA Combinatorics Seminar

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Lecture 25 - Approximation Algorithms

This is Lecture 25 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/lecture26.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

Related pages

Discrete Applied Mathematics | K-vertex-connected graph | Connectivity (graph theory) | Intersection graph | Generalized Petersen graph | Line graph | Perfect matching | Planar graph | Discrete Mathematics (journal) | Rook's graph | Polyhedral graph | Pentagonal prism | Triangular prism | Electronic Journal of Combinatorics | Simplicial polytope | Claw-free graph | Dürer graph | Regular graph | Complement (set theory) | Euler characteristic | Degree (graph theory) | Girth (graph theory) | Vertex cover | Simple polytope | Triangulation (geometry) | Graph theory | Cluster graph | Complete bipartite graph | Induced subgraph | Cycle graph | Deltahedron | Complete graph | Cubic graph | Snub disphenoid | Clique complex | Clique cover | Utility graph | Bridge (graph theory) | Independent set (graph theory) | Critical graph | Journal of Combinatorial Theory | Ars Combinatoria (journal) | Y-Δ transform | Simplicial complex | Rooted product of graphs