Book Section records
https://feeds.library.caltech.edu/people/Conlon-David/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 17:55:37 +0000Graph removal lemmas
https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001516
Authors: Conlon, David; Fox, Jacob
Year: 2013
DOI: 10.1017/cbo9781139506748.002
The graph removal lemma states that any graph on n vertices with o(n^h) copies of a fixed graph H on h vertices may be made H-free by removing o(n^2) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and computer science. In this survey we discuss these lemmas, focusing in particular on recent improvements to their quantitative aspects.https://authors.library.caltech.edu/records/kk69w-7xs20Combinatorial theorems relative to a random set
https://resolver.caltech.edu/CaltechAUTHORS:20190820-164721413
Authors: Conlon, David
Year: 2014
DOI: 10.48550/arXiv.1404.3324
We describe recent advances in the study of random analogues of combinatorial theorems.https://authors.library.caltech.edu/records/6xzh8-1ca79Recent developments in graph Ramsey theory
https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959899
Authors: Conlon, David; Fox, Jacob; Sudakov, Benny
Year: 2015
DOI: 10.1017/cbo9781316106853.003
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring of the edges of K_N contains a monochromatic copy of H. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics. In this survey, we will describe some of this progress.https://authors.library.caltech.edu/records/7tq4m-xda06A Note on Induced Ramsey Numbers
https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959255
Authors: Conlon, David; Dellamonica, Domingos; La Fleur, Steven; Rödl, Vojtěch; Schacht, Mathias
Year: 2017
DOI: 10.1007/978-3-319-44479-6_13
The induced Ramsey number r_(ind)(F) of a k-uniform hypergraph F is the smallest natural number n for which there exists a k-uniform hypergraph G on n vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of F. We study this function, showing that r_(ind)(F) is bounded above by a reasonable power of r(F). In particular, our result implies that r_(ind)(F) ≤ 2_(2_(ct)) for any 3-uniform hypergraph F with t vertices, mirroring the best known bound for the usual Ramsey number. The proof relies on an application of the hypergraph container method.https://authors.library.caltech.edu/records/4evw2-jxc52