A. Gordeev

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math.CO2026

Bollobás-Meir TSP Conjecture Holds Asymptotically

Alexey Gordeev

In 1992, Bollobás and Meir showed that for every $k \geq 1$ there exists a constant $c_{k}$ such that, for any $n$ points in the $k$ -dimensional unit cube $[0, 1]^{k}$ , one can find a…

math.CO2022

Erd\H os--Hajnal problem for $H$ -free hypergraphs

Danila Cherkashin, Alexei Gordeev, Georgii Strukov

This paper deals with the minimum number $m_{H} (r)$ of edges in an $H$ -free graph with the chromatic number more than $r$ . We show how bounds on Ramsey and Turán numbers imply bounds…

Bollobás-Meir TSP Conjecture Holds Asymptotically

Erd\H os--Hajnal problem for H-free hypergraphs

Erd\H os--Hajnal problem for $H$ -free hypergraphs