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Benny Sudakov studies combinatorics, especially extremal and probabilistic questions. His ETH author page documents work in these areas.^[ref]

With David Conlon, Jacob Fox and Choongbum Lee, he developed bounds for ordered Ramsey numbers. Their work compares the order-preserving problem with the ordinary Ramsey number and demonstrates a large gap for some ordered matchings.^[ref]

Choongbum Lee works on graph theory and Ramsey theory. His joint paper with David Conlon, Jacob Fox and Benny Sudakov investigates copies of a graph whose vertex order must be preserved.^[ref]

The ordered setting is sensitive to labeling: some ordered matchings have superpolynomial Ramsey numbers. Thus low ordinary degree does not by itself make an order-constrained embedding problem easy.^[ref]

David Conlon studies extremal graph theory and Ramsey theory. His joint work with Jacob Fox, Choongbum Lee and Benny Sudakov shows that imposing a vertex order can make Ramsey problems substantially harder, even for matchings.^[ref]

With Joonkyung Lee and Alexander Sidorenko, he also linked failures of a hypergraph analogue of the Sidorenko conjecture to improved extremal lower bounds. This turns a failed density inequality into information about constructions avoiding a specified hypergraph.^[ref]

Jacob Fox works on extremal combinatorics, Ramsey theory and algebraic and probabilistic methods in graph theory. His Stanford research page also identifies applications to computer science.^[ref]

With David Conlon, Choongbum Lee and Benny Sudakov, he studied ordered Ramsey numbers. Requiring the vertices of a monochromatic copy to appear in a prescribed order can force superpolynomial growth even when the underlying graph is a matching.^[ref]