J. Polcyn

activity

20152020

most citedPaths in hypergraphs: a rescaling phenomenon

2 citations · 3 across the 6 of their papers we have counts for

collaborators

8 papers

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

Minimum pair degree condition for tight Hamiltonian cycles in $4$ -uniform hypergraphs

Joanna Polcyn, Christian Reiher, Vojtěch Rödl +3

We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9 + o (1)) n^{2} /2$ contains a tight Hamiltonian cycle. This degree condition is asymptotic…

math.CO2020

The Ramsey number of a long even cycle versus a star

Peter Allen, Tomasz Łuczak, Joanna Polcyn +1

We find the exact value of the Ramsey number $R (C_{2 ℓ}, K_{1, n})$ , when $ℓ$ and $n = O (ℓ^{10/9})$ are large. Our result is closely related to the behaviour of Turán number $e…

math.CO2017★ 1 cited

The multipartite Ramsey number for the 3-path of length three

Tomasz Luczak, Joanna Polcyn

We study the Ramsey number for the 3-path of length three and $n$ colors and show that $R (P_{3}^{3}; n) \leq λ_{0} n + 7 n$ , for some explicit constant $λ_{0} = 1.97466 \dots$ .

math.CO2017★ 2 cited

Paths in hypergraphs: a rescaling phenomenon

Tomasz Luczak, Joanna Polcyn

Let $P_{ℓ}^{k}$ denote the loose $k$ -path of length $ℓ$ and let define $f_{ℓ}^{k} (n, m)$ as the minimum value of $Δ (H)$ over all $P_{ℓ}^{k}$ -free $k$ -graphs $H$ with $n$ vertices an…

math.CO2017

On multicolor Ramsey numbers for loose $k$ -paths of length three

Tomasz Łuczak, Joanna Polcyn, Andrzej Ruciński

We show that there exists an absolute constant $A$ such that for each $k \geq 2$ and every coloring of the edges of the complete $k$ -uniform hypergraph on $A r$ vertices with $r$ colo…

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

Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs

The Ramsey number of a long even cycle versus a star

The multipartite Ramsey number for the 3-path of length three

Paths in hypergraphs: a rescaling phenomenon

On multicolor Ramsey numbers for loose k-paths of length three

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

Minimum pair degree condition for tight Hamiltonian cycles in $4$ -uniform hypergraphs

On multicolor Ramsey numbers for loose $k$ -paths of length three