Computational problems in graph theory | Covering problems | NP-complete problems
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved by a polynomial-time algorithm if P ≠ NP. Moreover, it is hard to approximate – it cannot be approximated up to a factor smaller than 2 if the unique games conjecture is true. On the other hand, it has several simple 2-factor approximations. It is a typical example of an NP-hard optimization problem that has an approximation algorithm. Its decision version, the vertex cover problem, was one of Karp's 21 NP-complete problems and is therefore a classical NP-complete problem in computational complexity theory. Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in parameterized complexity theory. The minimum vertex cover problem can be formulated as a half-integral, linear program whose dual linear program is the maximum matching problem. Vertex cover problems have been generalized to hypergraphs, see Vertex cover in hypergraphs. (Wikipedia).
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
Complement of Independent Set is Vertex Cover | Graph Theory
We prove the complement of an independent vertex set is a vertex cover. This makes for an easy direct proof once we recall our definitions. An independent vertex set is a set of vertices, no two of which are adjacent. A vertex cover is a set of vertices such that every edge has at least on
From playlist Graph Theory
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
Complement of Vertex Cover is Independent Vertex Set | Graph Theory
We prove the complement of a vertex cover is an independent vertex set. Recall a vertex cover is a set of vertices covering all edges of the graph, meaning every edge has at least one end vertex in the cover. As a result, the complement of a cover cannot possible have two vertices joined b
From playlist Graph Theory
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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
Area and Perimeter of Geometric Figures
Worked out examples involving area and perimeter.
From playlist Geometry
A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally bi-continuos. The infinite spiral is for example a covering of the circle. Notice how every path on the circle can be lifted to the spiral. If a coveri
From playlist Algebraic Topology
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From playlist Geometry
CSE 373 -- Lecture 25, Fall 2020
From playlist CSE 373 -- Fall 2020
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
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
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
River Crossings (and Alcuin Numbers) - Numberphile
Discussing vertex covers and Alcuin numbers for graphs - and a famous old puzzle. Filmed at MSRI with Dr Annie Raymond. More links & stuff in full description below ↓↓↓ Annie Raymond: https://www.msri.org/people/38568 The Alcuin Number of a Graph: https://link.springer.com/chapter/10.100
From playlist Women in Mathematics - Numberphile
Breakdown of the basic components of graphs in graph theory
From playlist Graph Theory