D. Cherkashin

activity

20242026

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6 papers · 1 filter

math.CO2026

On uniform eventowns

Danila Cherkashin, Pavel Prozorov

Suppose that $n = 2 m$ , $k = 2 t$ and $n > 10 k^{7}$ . We show that if a family $F$ of $k$ -subsets of an $n$ -set has only even pairwise intersections then $|\mathcal F| \leq \binom…

math.CO2026

Short proofs of three combinatorial results in the Johnson scheme

Danila Cherkashin, Yakov Shubin

In this note, we give short proofs of three theorems concerning extremal problems in the Johnson scheme, or, in other terminology, on $(n, k, L)$ -systems. The main result is a proof…

math.CO2025

On the chromatic numbers of Johnson type graphs

Danila Cherkashin

A Johnson type graph $J_{\pm} (n, k, t)$ is a graph whose vertex set consists of vectors from ${- 1, 0, 1}^{n}$ of the length $k$ and edges connect vertices with scalar product $t…

math.CO2025

The number of trees in distance-hereditary graphs and their friends

Danila Cherkashin, Pavel Prozorov

Counting the number of spanning trees in specific classes of graphs has attracted increasing attention in recent years. In this note, we present unified proofs and generalizations…

math.CO2024

On set systems without singleton intersections

Danila Cherkashin

Consider a family $F$ of $k$ -subsets of an ambient $(k^{2} - k + 1)$ -set such that no pair of $k$ -subsets in $F$ intersects in exactly one element. In this short note…

math.CO2024

On the chromatic numbers of 3-dimensional slices

D. D. Cherkashin, A. J. Kanel-Belov, G. A. Strukov +1

We prove that for an arbitrary $ε > 0$ holds \[ Ï(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $I ¨ (M)$ stands for the chromatic number of an (infinite) graph…