6 citations · 21 across the 27 of their papers we have counts for
32 papers
Uniformity of extremal graph-codes
Noé de Rancourt, Pandelis Dodos, Konstantinos Tyros
It is an important fact that extremal discrete structures -- that is, discrete structures of maximal size among those that avoid certain configurations -- exhibit strong pseudorand…
Metric Poincaré inequalities for graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matoušek'…
Discrete Poincaré inequalities and universal approximators for random graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable al…
A universal threshold for geometric embeddings of trees
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
A graph is geometrically embeddable into a normed space when there is a mapping such that if and only if , for…
A combinatorial approach to nonlinear spectral gaps
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete Poincaré inequality for scalar functions, also sat…
A Dual Ramsey theorem for trees
Stevo Todorcevic, Konstantinos Tyros
We prove a dualization of the Graham--Rothschild Theorem for variable words indexed by homogeneous trees.