S. Kiselev

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20182021

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4 papers · 1 filter

math.CO2021

On the maximum number of distinct intersections in an intersecting family

Peter Frankl, Sergei Kiselev, Andrey Kupavskii

For $n > 2 k \geq 4$ we consider intersecting families $F$ consisting of $k$ -subsets of ${1, 2, \dots, n}$ . Let $I (F)$ denote the family of all distinc…

math.CO2020

VC-saturated set systems

Nóra Frankl, Sergei Kiselev, Andrey Kupavskii +1

The well-known Sauer lemma states that a family $F \subseteq 2^{[n]}$ of VC-dimension at most $d$ has size at most $\sum_{i = 0}^{d} (i n)$ . We obtain both random and ex…

math.CO2020

Rainbow matchings in $k$ -partite hypergraphs

Sergei Kiselev, Andrey Kupavskii

In this paper, we prove a conjecture of Aharoni and Howard on the existence of rainbow (transversal) matchings in sufficiently large families $F_{1}, \dots, F_{s}$ of…

math.CO2018

Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs

Jozsef Balogh, Danila Cherkashin, Sergei Kiselev

We suggest a new method on coloring generalized Kneser graphs based on hypergraphs with high discrepancy and small number of edges. The main result is providing a proper coloring o…

On the maximum number of distinct intersections in an intersecting family

VC-saturated set systems

Rainbow matchings in k-partite hypergraphs

Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs

Rainbow matchings in $k$ -partite hypergraphs