Chidambaram Annamalai: Finding Perfect Matchings in Bipartite Hypergraphs
Haxell's condition is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perfect matching in the bipartite hypergrap
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Raffaella Mulas - Spectral theory of hypergraphs
Hypergraphs are a generalization of graphs in which vertices are joined by edges of any size. In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra. We discuss the geometrical meaning of the largest an
From playlist Research Spotlight
Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs
Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob
From playlist TDA: Tutte Institute & Western University - 2021
We are given a bipartite graph where each vertex has a strict preference list ranking its neighbors. A matching M is stable if there is no unmatched pair ab, so that a and b both prefer each other to their partners in M. A matching M is popular if there is no matching M' such that the num
From playlist HIM Lectures 2015
Fractional Perfect Matchings in Hypergraphs - Andrzej Rucinski
Andrzej Rucinski Adam Mickiewicz University in Polznan, Poland; Emory University November 15, 2010 A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices is a set of n/k disjoint edges of H, while a fractional perfect matching in H is a function w : E → [0, 1] such that for
From playlist Mathematics
Matchings, Perfect Matchings, Maximum Matchings, and More! | Independent Edge Sets, Graph Theory
What are matchings, perfect matchings, complete matchings, maximal matchings, maximum matchings, and independent edge sets in graph theory? We'll be answering that great number of questions in today's graph theory video lesson! A matching in a graph is a set of edges with no common end-ve
From playlist Graph Theory
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
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)
Hypergraph matchings and designs – Peter Keevash – ICM2018
Combinatorics Invited Lecture 13.10 Hypergraph matchings and designs Peter Keevash Abstract: We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of d
From playlist Combinatorics
Catherine Greenhill (UNSW), The small subgraph conditioning method and hypergraphs, 26th May 2020
Speaker: Catherine Greenhill (UNSW) Title: The small subgraph conditioning method and hypergraphs Abstract: The small subgraph conditioning method is an analysis of variance technique which was introduced by Robinson and Wormald in 1992, in their proof that almost all cubic graphs are Ha
From playlist Seminars
The threshold for the square of a Hamilton cycleJinyoung Park
Computer Science/Discrete Mathematics Seminar II Topic: The threshold for the square of a Hamilton cycle Speaker: Jinyoung Park Affiliation: Member, School of Mathematics Date: October 20, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Extremal Problems for Uniformly Dense Hypergraphs - Mathias Schacht
Computer Science/Discrete Mathematics Seminar I Topic: Extremal Problems for Uniformly Dense Hypergraphs Speaker: Mathias Schacht Affiliation: Universität Hamburg Date: March 20, 2023 Extremal combinatorics is a central research area in discrete mathematics. The field can be traced back
From playlist Mathematics
More designs - P. Keevash - Workshop 1 - CEB T1 2018
Peter Keevash (Oxford) / 01.02.2018 We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge dat
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Wolfram Physics Project: Solving the Einstein Equations & Other PDEs Tuesday, Mar. 9, 2021
This is a Wolfram Physics Project working session on solving the Einstein equations and other PDE's in the Wolfram Model. Begins at 1:18 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check ou
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics II: Emergent Hypergraph Geometry and General Relativity
Find more information about the summer school here: https://education.wolfram.com/summer/school Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announcement Find the tools to build a universe: https:
From playlist Wolfram Summer Programs
Algebra Ch 40: Hyperbolas (1 of 10) What is a Hyperbola?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn a hyperbola is a graph that result from meeting the following conditions: 1) |d1-d2|=constant (same number) 2) the grap
From playlist THE "HOW TO" PLAYLIST
DSI | Hypergraphs and Topology for Data Science | By Emilie Purvine
Data scientists and applied mathematicians must grapple with complex data when analyzing complex systems. Analytical methods almost always represent phenomena as a much simpler level than the complex structure or dynamics inherent in systems, through either simpler measured or sampled data
From playlist DSI Virtual Seminar Series
On the Conjectures of Nonnegative kk-Sum and Hypergraph Matching - Hao Huang
Hao Huang University of California, Los Angeles; Member, School of Mathematics October 9, 2012 A twenty-year old conjecture by Manickam, Mikl\'os, and Singhi asked whether for any integers n,kn,k satisfying n≥4kn≥4k, every set of nn real numbers with nonnegative sum always has at least
From playlist Mathematics