Graph theory | Rainbow problems
In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions: * It is an independent set – every two vertices in U are not adjacent (there is no edge between them); * It is a rainbow set – U contains at most a single vertex from each color Vi. Other terms used in the literature are independent set of representatives, independent transversal, and independent system of representatives. As an example application, consider a faculty with m departments, where some faculty members dislike each other. The dean wants to construct a committee with m members, one member per department, but without any pair of members who dislike each other. This problem can be presented as finding an ISR in a graph in which the nodes are the faculty members, the edges describe the "dislike" relations, and the subsets V1, …, Vm are the departments. (Wikipedia).
Every Subset of a Linearly Independent Set is also Linearly Independent Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.
From playlist Proofs
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Power Sets and the Cardinality of the Continuum
Get better at math with Brilliant ► http://www.brilliant.org/treforbazett. Sign up for free, or the first 200 people who sign up using that link get 20% off an annual premium subscription. My thanks to Brilliant for sponsoring today's video! In this video we will learn about the power se
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Independent Vertex Sets | Graph Theory, Maximal and Maximum Independent Sets
What are independent vertex sets in graph theory? We'll go over independent sets, their definition and examples, and some related concepts in today's video graph theory lesson! A subset of the vertex set of a graph is an independent vertex set if and only if it contains no pair of adjace
From playlist Set Theory
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
From Robust Sublinear Expanders to Additive Number Theory via Rainbow Cycles - Matija Bucic
Computer Science/Discrete Mathematics Seminar II Topic: From Robust Sublinear Expanders to Additive Number Theory via Rainbow Cycles Speaker: Matija Bucic Affiliation: Veblen Research Instructor, School of Mathematics Date: February 21, 2023 Robust sublinear expansion represents a fairl
From playlist Mathematics
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
Is the Empty Set an Independent Vertex Set? | Graph Theory Exercises
We prove the empty set is an independent set using the definition of independent vertex sets. We also show the empty set is an independent set by considering the complement of a vertex cover. Recall that an independent vertex set S of a graph G is a subset of the vertex set of G such that
From playlist Graph Theory Exercises
Rainbow structures, Latin squares & graph decompositions - Benny Sudakov
Computer Science/Discrete Mathematics Seminar I Topic: Rainbow structures, Latin squares & graph decompositions Speaker: Benny Sudakov Affiliation: ETH Zürich Date: March 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Rainbow Matchings in Hypergraphs - Cosmin Pohoata
Computer Science/Discrete Mathematics Seminar II Topic: Rainbow Matchings in Hypergraphs Speaker: Cosmin Pohoata Affiliation: IAS - Member, School of Mathematics Date: February 14, 2023 Suppose we are given matchings M1,....,MN of size t in some r-uniform hypergraph, and let us think of
From playlist Mathematics
Arithmetic regularity, removal, and progressions - Jacob Fox
Title: Marston Morse Lectures Topic: Arithmetic regularity, removal, and progressions Speaker: Jacob Fox Affiliation: Stanford University Date: Oct 25, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
الاهتزازات والأمواج (جامعة إم آي تي) - المحاضرة 22: قوس قزح، الهالات، التألقات
MIT المحاضرة الثانية والعشرون من مساق "الاهتزازات والأمواج" من جامعة إم آي تي للبروفيسور والتر لوين وهي عن قوس قزح، الهالات، التألقات بالإضافة للفيديو هناك ملفات مرفقة على موقعنا الالكتروني https://shamsunalarabia.net/courses/الاهتزازات-والأمواج/ رابط المساق https://www.youtube.com/watch?
From playlist 8.03 Arabic Subtitles
Pablo Soberón on Tverberg-type results, weak epsilonnets and the probabilistic method
Date: March 16, 2018 Location: Worldwide Center of Mathematics Abstract: During this talk we will discuss some robust variations of Tverberg’s theorem. The aim is to seek partitions of a finite set of points in R^d such that the convex hulls of the parts intersect, even if our set of point
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Lec 22: Rainbows, Haloes, Coronae, Glories | 8.03 Vibrations and Waves, Fall 2004 (Walter Lewin)
Bring a friend and an umbrella! A rainbow will appear! - The Physics behind the Mystery Picture will be revealed. This lecture is part of 8.03 Physics III: Vibrations and Waves, as taught in Fall 2004 by Dr. Walter Lewin at MIT. This video was formerly hosted on the YouTube channel MIT O
From playlist 8.03 Vibrations and Waves - CosmoLearning.com Physics
Rob Ashton: Got Make? | JSConf EU 2014
Everybody loves the Gruntfile, except for those who have seen the True Path and are now creating everything in Gulp, except for those of us that simply don’t understand the fuss because Make has “done all of that for years”. Make gets an awful rap for being obtuse and difficult to underst
From playlist JSConf EU 2014
Michal Pilipczuk: Introduction to parameterized algorithms, lecture II
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
Math 060 Linear Algebra 10 092914: Vector Space Bases
Basis; dimension; cardinality of a linearly independent set cannot exceed that of a spanning set; if a set has the same cardinality as the dimension of the vector space, then linear independence is equivalent to that set spanning the vector space; any linear independent set can be extended
From playlist Course 4: Linear Algebra
Yip Harburg: Forgotten Lyricist of 'Over the Rainbow'
Edgar "Yip" Harburg wrote the lyric for "Over the Rainbow", one of the most beloved movie film songs of all time. Yet so few people remember his name. The History Guy remembers the life and legacy of Harburg, the man who also wrote the lyric for the song considered the anthem of the Great
From playlist History without War