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
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"
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
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
Proof: Regular Bipartite Graph has a Perfect Matching | Graph Theory
An r-regular bipartite graph, with r at least 1, will always have a perfect matching. We prove this result about bipartite matchings in today's graph theory video lesson using Hall's marriage theorem for bipartite matchings. Recall that a perfect matching is a matching that covers every ve
From playlist Graph Theory
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
Parallels and the double triangle | Universal Hyperbolic Geometry 18 | NJ Wildberger
We discuss Euclid's parallel postulate and the confusion it led to in the history of hyperbolic geometry. In Universal Hyperbolic Geometry we define the parallel to a line through a point, NOT the notion of parallel lines. This leads us to the useful construction of the double triangle of
From playlist Universal Hyperbolic Geometry
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
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
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
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
8ECM Invited Lecture: Daniela Kühn
From playlist 8ECM Invited Lectures
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
Two conjectures of Ringel, by Katherine Staden
CMSA Combinatorics Seminar, 22 July 2020
From playlist CMSA Combinatorics Seminar
Pattern Matching - Correctness
Learn how to use pattern matching to assist you in your determination of correctness. This video contains two examples, one with feedback and one without. https://teacher.desmos.com/activitybuilder/custom/6066725595e2513dc3958333
From playlist Pattern Matching with Computation Layer
Thresholds Versus Fractional Expectation-Thresholds - Keith Frankston
Computer Science/Discrete Mathematics Seminar I Topic: Thresholds Versus Fractional Expectation-Thresholds Speaker: Keith Frankston Affiliation: Rutgers University Date: December 16, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Members’ Colloquium Topic: Thresholds Speaker: Jinyoung Park Affiliation: Stanford University Date: May 16, 2022 Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for
From playlist Mathematics
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
Duality and perpendicularity | Universal Hyperbolic Geometry 9 | NJ Wildberger
Perpendicularity in universal hyperbolic geometry is defined in terms of duality. One big difference with classical HG is that points can also be perpendicular, not just lines. Once we have perpendicularity, we can define altitudes. We also state the collinear points theorem and concurrent
From playlist Universal Hyperbolic Geometry