Konstantin E. Tikhomirov

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20242026

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3 papers · 1 filter

math.CO2026

Online Beck--Fiala Down to Logarithmic Sparsity

Dylan J. Altschuler, Konstantin Tikhomirov

The Beck--Fiala conjecture asserts that every matrix $A \in {0, 1}^{n \times T}$ with at most $d$ nonzero entries in each column has discrepancy $O (d)$ . A major breakthrough re…

math.CO2025

A universal threshold for geometric embeddings of trees

Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1

A graph $G = (V, E)$ is geometrically embeddable into a normed space $X$ when there is a mapping $ζ : V \to X$ such that $∥ ζ (v) - ζ (w) ∥_{X} ⩽ 1$ if and only if ${v, w} \in E$ , for…

math.CO2024

Locally seeded embeddings, and Ramsey numbers of bipartite graphs with sublinear bandwidth

Dylan J. Altschuler, Han Huang, Konstantin Tikhomirov

A seminal result of Lee asserts that the Ramsey number of any bipartite $d$ -degenerate graph $H$ satisfies $lo g r (H) = lo g n + O (d)$ . In particular, this bound applies to every b…