Andrzej Żak

activity

20152026

collaborators

5 papers

math.CO2026

The Erdős four-edge intersection problem

Andrzej Żak

For an $n$ -vertex graph $G$ and a permutation $σ$ of its vertex set, let $σ (G)$ denote the corresponding relabelling of $G$ , and put \[ I_G(σ)=|E(G)\cap E(σ(G))|. \] Let $f (n, k)$ b…

math.CO2026

An asymptotic solution to the Erdős four-edge intersection problem

Andrzej Żak

For an $n$ -vertex graph $G$ and a permutation $σ$ of its vertex set, let $σ (G)$ denote the corresponding relabelling of $G$ , and put $I_{G} (σ) = ∣ E (G) \cap E (σ (G)) ∣$ . Let $f (n, k)$ be th…

math.CO2021

Constructing sparsest $ℓ$ -hamiltonian saturated $k$ -uniform hypergraphs for a wide range of $ℓ$

Andrzej Ruciński, Andrzej Żak

Given $k \geq 3$ and $1 \leq ℓ < k$ , an $(ℓ, k)$ -cycle is one in which consecutive edges, each of size $k$ , overlap in exactly $ℓ$ vertices. We study the smallest number of edge…

math.CO2018

A note on packing of uniform hypergraphs

Jerzy Konarski, Andrzej Żak, Mariusz Woźniak

A packing of two $k$ -uniform hypergraphs $H_{1}$ and $H_{2}$ is a set ${H_{1}^{'}, H_{2}^{'}}$ of edge-disjoint sub-hypergraphs of the complete $k$ -uniform hypergraph $K_{n}^{(k)}$ such that $H_…

math.CO2015

Packing large trees of consecutive orders

Andrzej Żak

A conjecture by Bollobás from 1995 (which is a weakenning of the famous Tree Packing Conjecture by Gyárfás from 1976) states that any set of $k$ trees $T_{n}, T_{n - 1}, \dots, T_{n - k + 1}$ …

The Erdős four-edge intersection problem

An asymptotic solution to the Erdős four-edge intersection problem

Constructing sparsest ℓ-hamiltonian saturated k-uniform hypergraphs for a wide range of ℓ

A note on packing of uniform hypergraphs

Packing large trees of consecutive orders

Constructing sparsest $ℓ$ -hamiltonian saturated $k$ -uniform hypergraphs for a wide range of $ℓ$