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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 3
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we give an example to illustrate how to use the hypergraph regularity lemmas. The absorbing method due to R?dl, Schacht and Szemerédi is a powerful tool in proving hypergraph Hamilton cy...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 2
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we first introduce the definitions of equitable partitions and state the hypergraph regularity lemma due to R?dl and Schacht. Then, we give the conception of reduced hypergraphs and its ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 1
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
Hypergraph regularity lemmas are generalizations of Szemerédi's regularity lemma for graphs, which has been proved to be a powerful tool with many subsequent. In this talk, we first give a brief intro...
The size of a hypergraph and its matching number
hypergraph its matching number Combinatorics
2011/9/22
Abstract: More than forty years ago, Erd\H{o}s conjectured that for any T <= N/K, every K-uniform hypergraph on N vertices without T disjoint edges has at most max{\binom{KT-1}{K}, \binom{N}{K} - \bin...
The condensation transition in random hypergraph 2-coloring
random structures phase transitions hypergraph 2-coloring second moment method
2011/9/5
Abstract: For many random constraint satisfaction problems such as random satisfiability or random graph or hypergraph coloring, the best current estimates of the threshold for the existence of soluti...
About maximal number of edges in hypergraph-clique with chromatic number 3
hypergraph-clique chromatic number 3 Combinatorics
2011/8/31
Abstract: Let $ H = (V,E) $ be a hypergraph. By the chromatic number of a hypergraph $ H = (V,E) $ we mean the minimum number $\chi(H)$ of colors needed to paint all the vertices in $ V $ so that any ...
We obtain a hypergraph generalisation of the graph blow-up lemma proved by Komlos, Sarkozy and Szemeredi, showing that hypergraphs with sufficient regularity and no atypical vertices behave as if they...
Computing the partition function for perfect matchings in a hypergraph
hypergraph perfect matching partition function permanent
2010/12/6
Given non-negative weights wS on the k-subsets S of a km-element set V , we consider the sum of the products wS1 · · ·wSm over all partitions V =S1 [ . . . [ Sm into pairwise disjoint k-subsets Si.
A Hypergraph Dictatorship Test with Perfect Completeness
Property testing Gowers norm Fourier analysis PCP
2012/12/3
A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based PCP construction.