Computational problems in graph theory | NP-complete problems
In graph theory, an edge dominating set for a graph G = (V, E) is a subset D ⊆ E such that every edge not in D is adjacent to at least one edge in D. An edge dominating set is also known as a line dominating set. Figures (a)–(d) are examples of edge dominating sets (thick red lines). A minimum edge dominating set is a smallest edge dominating set. Figures (a) and (b) are examples of minimum edge dominating sets (it can be checked that there is no edge dominating set of size 2 for this graph). (Wikipedia).
Dominating Sets and Domination Number of Graphs | Graph Theory
A vertex is said to dominate itself and its neighbors. Then, a dominating set of a graph G is a vertex subset S of G such that every vertex in G is dominated by some vertex in S. This means every vertex in G-S is adjacent to some vertex in S. A dominating set of minimum cardinality is a mi
From playlist Graph Theory
How to find DOMINATING STRATEGIES with Game Theory
Check out Brilliant ► https://brilliant.org/TreforBazett/ Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory. Check out Episodes 1 & 2 of the Game Theory Playlist ► https://www.youtub
From playlist Game Theory
Game of Thrones: Balance of Power Over Time
Data visualization showing the balance of power in Game of Thrones over time . "Balance of Power" in this video essentially means how far a given character is from sitting on the iron throne at any point in time. Note that for all characters other than those actually sitting on the throne,
From playlist Data Visualizations
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
This video covers the properties of limits and verifies them graphically.
From playlist Limits
Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p
From playlist Set Theory
How to Compute a One Sided limit as x approaches from the right
In this video I will show you How to Compute a One Sided limit as x approaches from the right.
From playlist One-sided Limits
Every Set is an Element of its Power Set | Set Theory
Every set is an element of its own power set. This is because the power set of a set S, P(S), contains all subsets of S. By definition, every set is a subset of itself, and thus by definition of the power set of S, it must contain S. This is even true for the always-fun empty set! We discu
From playlist Set Theory
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
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
Siddharth Pritam (8/10/22): Swap, Shift and Trim to Edge Collapse a Flag Filtration
Boissonnat and Pritam [SoCG'20] introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method requir
From playlist AATRN 2022
Math Exposition Video 1:Introduction to the Probabilistic Method
This video is (hopefully) going to be part of a series of me tyring to explain mathematics close to my heart :-) This is also going to be my maiden entry into 3Blue1Brown's Summer of Math Exposition. I talk about a couple of intriguing examples,one on Ramsey numbers and the other on domina
From playlist Summer of Math Exposition Youtube Videos
AMMI 2022 Course "Geometric Deep Learning" - Seminar 1 (Physics-based GNNs) - Francesco Di Giovanni
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 Seminar 1 - Graph neural networks through the lens of multi-particle dynamics and gradient flows - Francesco Di Giovanni (Twitter) Slides: https://www.dropbox.com/s/
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
[BOURBAKI 2017] 11/03/2017 - 3/4 - Patrick MASSOT
Patrick MASSOT — Flexibilité en géométrie de contact en grande dimension [d'après Borman, Eliashberg et Murphy] Les structures de contact sont des champs d'hyperplans apparaissant naturellement au bord de variétés symplectiques ou holomorphes et dont l'attrait provient d'un subtil mélang
From playlist BOURBAKI - 2017
Maria Chudnovsky: Coloring graphs with forbidden induced paths
Abstract: The problem of testing if a graph can be colored with a given number k of colors is NP-complete for every k[greater than]2. But what if we have more information about the input graph, namely that some fixed graph H is not present in it as an induced subgraph? It is known that the
From playlist Combinatorics
Paolo Boldi - Axioms for centrality: rank monotonicity for PageRank
https://indico.math.cnrs.fr/event/3475/attachments/2180/2562/Boldi_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
Here we show a quick way to set up a face in desmos using domain and range restrictions along with sliders. @shaunteaches
From playlist desmos
An Introduction to Lifted Expander Graphs - Fernando Granha Jeronimo
Computer Science/Discrete Mathematics Seminar II Topic: An Introduction to Lifted Expander Graphs Speaker: Fernando Granha Jeronimo Affiliation: Member, School of Mathematics Date: December 14, 2021 Expander graphs are sparse and yet well-connected graphs. Several applications in theoret
From playlist Mathematics