D. Zakharov

activity

20162021

collaborators

Showing math.COShow all

7 papers · 1 filter

math.CO2021

Norm hypergraphs

Cosmin Pohoata, Dmitriy Zakharov

We introduce a high uniformity generalization of the so-called (projective) norm graphs of Alon, Kollár, Rónyai, and Szabó, and use it to show that $$\operatorname{ex}_{d}(n,K_{s_{…

math.CO2020

Random multilinear maps and the Erdős box problem

David Conlon, Cosmin Pohoata, Dmitriy Zakharov

By using random multilinear maps, we provide new lower bounds for the Erdős box problem, the problem of estimating the extremal number of the complete $d$ -partite $d$ -uniform hyper…

math.CO2020

The extremal number of surfaces

Andrey Kupavskii, Alexandr Polyanskii, István Tomon +1

In 1973, Brown, Erdős and Sós proved that if $H$ is a 3-uniform hypergraph on $n$ vertices which contains no triangulation of the sphere, then $H$ has at most $…

math.CO2020

Turán-type results for intersection graphs of boxes

István Tomon, Dmitriy Zakharov

In this short note, we prove the following analog of the Kővári-Sós-Turán theorem for intersection graphs of boxes. If $G$ is the intersection graph of $n$ axis-parallel boxes in $…

math.CO2020

Zero subsums in vector spaces over finite fields

Cosmin Pohoata, Dmitriy Zakharov

The Olson constant $O L (F_{p}^{d})$ represents the minimum positive integer $t$ with the property that every subset $A \subset F_{p}^{d}$ of cardinality $…

math.CO2018

Chromatic numbers of Kneser-type graphs

Dmitriy Zakharov

Let $G (n, r, s)$ be a graph whose vertices are all $r$ -element subsets of an $n$ -element set, in which two vertices are adjacent if they intersect in exactly $s$ elements. In this…

math.CO2016

Regular bipartite graphs and intersecting families

Andrey Kupavskii, Dmitriy Zakharov

In this paper we present a simple unifying approach to prove several statements about intersecting and cross-intersecting families, including the Erd\H os--Ko--Rado theorem, the Hi…