T. Luczak

activity

19932023

most citedUnmodulated spin chains as universal quantum wires

241 citations · 498 across the 19 of their papers we have counts for

collaborators

23 papers

math.CO2023

On size Ramsey numbers for a pair of cycles

Małgorzata Bednarska-Bzdęga, Tomasz Łuczak

We show that there exists an absolute constant $A$ such that the size Ramsey number of a pair of cycles $(C_{n}$ , $C_{2 d})$ , where $4 \leq 2 d \leq n$ , is bounded from above by $A n$ . We a…

math.CO2023

The next case of Andrásfai's conjecture

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

Let $ex (n, s)$ denote the maximum number of edges in a triangle-free graph on $n$ vertices which contains no independent sets larger than $s$ . The behaviour of $\mathrm{ex}…

math.CO2022

On the restricted size Ramsey number for a pair of cycles

Tomasz Łuczak, Joanna Polcyn, Zahra Rahimi

For graphs $H_{1}, H_{2}$ by $r^{*} (H_{1}, H_{2})$ we denote the minimum number of edges in a graph $G$ on $r (H_{1}, H_{2})$ vertices such that $G \to (H_{1}, H_{2})$ . We show that for each pair of natur…

math.CO2020

Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree

Tomasz Łuczak, Zahra Rahimi

We show that for every $η > 0$ , there exists $n_{0}$ such that for every even $n$ , $n \geq n_{0}$ , and every graph $G$ with $(2 + η) n$ vertices and minimum degree at least $(7/4 + 4 η) n$ , each…

math.CO2017★ 1 cited

A tale of stars and cliques

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

We show that for an infinitely many natural numbers $k$ there are $k$ -uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}…

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 $λ_{0} = 1.97466 \dots$ .