Andrzej Rucinski

activity

20202026

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2026

Rainbow Turán numbers for paths of length four

Sylwia Antoniuk, Andrzej Grzesik, Magdalena Prorok +1

Given a set $V$ of $n$ vertices and an integer $k \geq 1$ , our goal is to maximize the number of edges in graphs $G_{1}, G_{2}, \dots, G_{k}$ , defined on $V$ , under the constraint that the…

math.CO2021

Tight multiple twins in permutations

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

Two permutations are similar if they have the same length and the same relative order. A collection of $r \geq 2$ disjoint, similar subsequences of a permutation $π$ form $r$ -twins in…

math.CO2020

On weak twins and up-and-down sub-permutations

Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński

Two permutations $(x_{1}, \dots, x_{w})$ and $(y_{1}, \dots, y_{w})$ are weakly similar if $x_{i} < x_{i + 1}$ if and only if $y_{i} < y_{i + 1}$ for all $1 ⩽ i ⩽ w$ . Let $π$ be a permutati…

math.CO2020

Sandwiching biregular random graphs

Tereza Klimošová, Christian Reiher, Andrzej Ruciński +1

Let $G (n, n, m)$ be a uniformly random $m$ -edge subgraph of the complete bipartite graph $K_{n, n}$ with bipartition $(V_{1}, V_{2})$ , where $n_{i} = ∣ V_{i} ∣$ . Given a real number $p \in [0,1…

math.CO2020

Turán and Ramsey numbers for $3$ -uniform minimal paths of length $4$

Jie Han, Joanna Polcyn, Andrzej Ruciński

We determine Turán numbers for the family of 3-uniform minimal paths of length four \emph{for all $n$ }. We also establish the second and third order Turán numbers and use them to c…

math.CO2020

Properly colored Hamilton cycles in Dirac-type hypergraphs

Sylwia Antoniuk, Nina Kamčev, Andrzej Ruciński

We consider a robust variant of Dirac-type problems in $k$ -uniform hypergraphs. For instance, we prove that if $H$ is a $k$ -uniform hypergraph with minimum codegree at least $(1/2…

Rainbow Turán numbers for paths of length four

Tight multiple twins in permutations

On weak twins and up-and-down sub-permutations

Sandwiching biregular random graphs

Turán and Ramsey numbers for 3-uniform minimal paths of length 4

Properly colored Hamilton cycles in Dirac-type hypergraphs

Turán and Ramsey numbers for $3$ -uniform minimal paths of length $4$