85 citations · 323 across the 14 of their papers we have counts for
8 papers · 1 filter
Andrásfai and Vega graphs in Ramsey-Turán theory
Tomasz Łuczak, Joanna Polcyn, Christian Reiher
Given positive integers , we let denote the maximum number of edges in a triangle-free graph on vertices with . In the early sixties…
On the Ramsey-Turán density of triangles
Tomasz Łuczak, Joanna Polcyn, Christian Reiher
One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graphs on vertices has at most edges. About half a cent…
Integral homology of random simplicial complexes
Tomasz Łuczak, Yuval Peled
The random -dimensional simplicial complex process starts with a complete graph on vertices, and in every step a new -dimensional face, chosen uniformly at random, is add…
Manipulative waiters with probabilistic intuition
Mał gorzata Bednarska-Bzdȩga, Dan Hefetz, Michael Krivelevich +1
For positive integers and and a monotone graph property $\cA$, we consider the two player, perfect information game $\WC(n,q,\cA)$, which is defined as follows. The game pr…
Coloring dense graphs via VC-dimension
Tomasz Łuczak, Stéphan Thomassé
The Vapnik-Červonenkis dimension is a complexity measure of set-systems, or hypergraphs. Its application to graphs is usually done by considering the sets of neighborhoods of the v…
Two critical periods in the evolution of random planar graphs
Mihyun Kang, Tomasz Łuczak
Let be a graph chosen uniformly at random from the family of all labeled planar graphs with vertices and edges. In the paper we study the component structure of $P…
On the Multi-coloured Ramsey Numbers of Cycles
Tomasz Łuczak, Miklós Simonovits, Jozef Skokan
For a graph and an integer , denotes the smallest integer for which for any edge-colouring of the complete graph by colours there exists a colou…
The Ramsey number for a triple of large cycles
Agnieszka Figaj, Tomasz Luczak
We find the asymptotic value of the Ramsey number for a triple of long cycles, where the lengths of the cycles are large but may have different parity.