D. Zakharov

activity

20162026

most citedEssentially tight bounds for rainbow cycles in proper edge-colourings

3 citations · 15 across the 35 of their papers we have counts for

collaborators

Showing 2022Show all

5 papers · 1 filter

math.CO2022

Sharp bounds for rainbow matchings in hypergraphs

Cosmin Pohoata, Lisa Sauermann, Dmitrii Zakharov

Suppose we are given matchings $M_{1}, ...., M_{N}$ of size $t$ in some $r$ -uniform hypergraph, and let us think of each matching having a different color. How large does $N$ need to be…

math.CO2022★ 1 cited

Cutting corners

Andrey Kupavskii, Arsenii Sagdeev, Dmitrii Zakharov

We say that a subset $M$ of $R^{n}$ is exponentially Ramsey if there are $ε > 0$ and $n_{0}$ such that $χ (R^{n}, M) \geq (1 + ε)^{n}$ for any $n > n_{0}$ , where $χ (R^{n}, M)$ stan…

math.CO2022★ 1 cited

Upper bounds for Heilbronn's triangle problem in higher dimensions

Dmitrii Zakharov

We develop a new simple approach to prove upper bounds for generalizations of the Heilbronn's triangle problem in higher dimensions. Among other things, we show the following: for…

math.CO2022★ 2 cited

Convex polytopes from fewer points

Cosmin Pohoata, Dmitrii Zakharov

Let $E S_{d} (n)$ be the smallest integer such that any set of $E S_{d} (n)$ points in $R^{d}$ in general position contains $n$ points in convex position. In 1960, Erdős and S…

math.CO2022★ 1 cited

Spread approximations for forbidden intersections problems

Andrey Kupavskii, Dmitriy Zakharov

We develop a new approach to approximate families of sets, complementing the existing ` $Δ$ -system method' and `junta approximations method'. The approach, which we refer to as `spr…