Graph families | Bipartite graphs
In the mathematical field of graph theory, an instance of the Steiner tree problem (consisting of an undirected graph G and a set R of terminal vertices that must be connected to each other) is said to be quasi-bipartite if the non-terminal vertices in G form an independent set, i.e. if every edge is incident on at least one terminal. This generalizes the concept of a bipartite graph: if G is bipartite, and R is the set of vertices on one side of the bipartition, the set to R is automatically independent. This concept was introduced by Rajagopalan and Vazirani who used it to provide a (3/2 + ε) approximation algorithm for the Steiner tree problem on such instances. Subsequently, the ε factor was removed by Rizzi and a 4/3 approximation algorithm was obtained by Chakrabarty et al.The same concept has been used by subsequent authors on the Steiner tree problem, e.g. Robins and Zelikovskyproposed an approximation algorithm for Steiner tree problem which on quasi-bipartite graphs has approximation ratio 1.28. The complexity of Robins and Zelikovsky's algorithm is O(m n2), where m and n are the numbers of terminals and non-terminals in the graph, respectively. Furthermore, Gröpl et al. gave a 1.217-approximation algorithm for the special case of uniformly quasi-bipartite instances. (Wikipedia).
What is a Bipartite Graph? | Graph Theory
What is a bipartite graph? We go over it in today’s lesson! I find all of these different types of graphs very interesting, so I hope you will enjoy this lesson. A bipartite graph is any graph whose vertex set can be partitioned into two disjoint sets (called partite sets), such that all e
From playlist Graph Theory
What are Complete Bipartite Graphs? | Graph Theory, Bipartite Graphs
What are complete bipartite graphs? We'll define complete bipartite graphs and show some examples and non-examples in today's video graph theory lesson! Remember a graph G = (V, E) is bipartite if the vertex set V can be partitioned into two sets V1 and V2 (called partite sets) such that
From playlist Graph Theory
Bipartite Graphs with Isolated Vertices | Graph Theory, Complete Bipartite Graphs
We know what a bipartite graph is, and we know about complete bipartite graphs. But how do these definitions work with isolated vertices that have no neighbors? We'll go over just that in today's graph theory lesson! Remember that a bipartite graph is a graph whose vertices that can be pa
From playlist Graph Theory
OCR MEI MwA D: Graph Theory: 07 Bipartite Graphs
https://www.buymeacoffee.com/TLMaths Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dea
From playlist OCR MEI MwA D: Graph Theory
From playlist Graph Theory
Bipartite Graphs: Determine a Matching of A if Possible
This video explains how to determine a matching of A in a bipartite and how to use Hall's Marriage theorem to explain why there I not a matching of A in a graph. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Every Tree is a Bipartite Graph
This video explains how to show that a tree is a bipartite graph. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Bipartite Graphs and Named Graphs
The lesson explains bipartite and complete bipartite graphs. Then common named graphs are defined. mathispower4u.com
From playlist Graph Theory (Discrete Math)
A Tight Bound for Hypergraph Regularity - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar I Topic: A Tight Bound for Hypergraph Regularity Speaker: Guy Moshkovitz Affiliation: Harvard University Date: Febuary 27, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Bipartite perfect matching is in quasi-NC - Fenner
Computer Science/Discrete Mathematics Seminar I Topic: Bipartite perfect matching is in quasi-NC Speaker: Stephen Fenner Date:Monday, February 8 We show that the bipartite perfect matching problem is in quasi 𝖭𝖢2quasi-NC2. That is, it has uniform circuits of quasi-polynomial size and O(
From playlist Mathematics
Dependent random choice - Jacob Fox
Marston Morse Lectures Topic: Dependent random choice Speaker: Jacob Fox, Stanford University Date: October 26, 2016 For more videos, visit http://video.ias.edu
From playlist Mathematics
PMSP - Quasi-random groups - Timothy Gowers
Timothy Gowers Cambridge University June 16, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
A Regularity Lemma with Modifications - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar II Topic: A Regularity Lemma with Modifications Speaker: Guy Moshkovitz Affiliation: Member, School of Mathematics Date: January 29, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Introduction to Matching in Bipartite Graphs (Hall's Marriage Theorem)
This video introduces matching in bipartite graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
A glimpse of continuous combinatorics via natural quasirandomness - Leonardo Coregliano
Short Talks by Postdoctoral Members Topic: A glimpse of continuous combinatorics via natural quasirandomness Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: September 23, 2021
From playlist Mathematics
13. Sparse regularity and the Green-Tao theorem
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX After discussion of Ramanujan graphs, Prof. Zhao discusse
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Cedric Koh: Beyond value iteration for parity games: strategy iteration with universal trees
Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (2017). The central combinatorial object underlying these approaches is a universal tree, as identified by Czerwi´nski et al. (2019). By providing a quasi-polynomial lower bou
From playlist Workshop: Tropical geometry and the geometry of linear programming
Examples of non-positively curved groups - Kim Ruane
Women and Mathematics Title: Examples of non-positively curved groups Speaker: Kim Ruane Affiliation: Tufts University Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
14. Graph limits I: introduction
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Graph limits provide a beautiful analytic framework for s
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019