14 citations · 14 across the 1 of their papers we have counts for
5 papers
Freiheitssatz and phase transition for the density model of random groups
Tsung-Hsuan Tsai
Magnus' Freiheitssatz states that if a group is defined by a presentation with generators and a single relator containing the last generating letter, then the first lette…
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…
Asymmetry and structural information in preferential attachment graphs
Tomasz Luczak, Abram Magner, Wojciech Szpankowski
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Where…