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1,726 claims from 1,063 papers are on the record. 46 have been checked so far; the other 1,680 have no check with a result yet.

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Status: Unchecked ×Keyword: explicit constructions ×Clear all

4 claims from 2 papers

1. Mathematics › Limits and Structures in Graph Theory

   Ramsey properties of algebraic graphs and hypergraphs

   Sudakov and Tomon · arXiv (Cornell University) · 2021

   The paper shows that algebraic graphs and hypergraphs with good Ramsey properties need at least one of the parameters n, d or m to be large, using algebraic, geometric and combinatorial tools.

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   1. UncheckedGraphs defined by low-complexity polynomials on N vertices contain a clique or independent set of size N^Ω(1/ndm), with similar results for hypergraphs.“We extend this result by showing that such $G$ contains either a clique or an independent set of size $N^{Ω(1/ndm)}$ and prove similar results for algebraic hypergraphs of constant complexity.”
   2. Unchecked“We also obtain a polynomial regularity lemma for $r$-uniform algebraic hypergraphs that are defined by a single polynomial, that might be of independent interest.”

2. Mathematics › Limits and Structures in Graph Theory

   Induced Ramsey-type theorems

   Fox and Sudakov · arXiv (Cornell University) · 2007

   Unchecked2 claims
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   1. Unchecked“The proofs are based on a simple lemma (generalizing one by Graham, Rodl, and Rucinski) that can be used as a replacement for Szemeredi's regularity lemma, thereby giving much better bounds.”
   2. Unchecked“The same approach can be also used to show that pseudo-random graphs have strong induced Ramsey properties.”