554 citations · 1.5k across the 71 of their papers we have counts for
83 papers
Large sumsets from medium-sized subsets
Bela Bollobas, Imre Leader, Marius Tiba
The classical Cauchy--Davenport inequality gives a lower bound for the size of the sum of two subsets of , where is a prime. Our main aim in this paper is to pro…
Large sumsets from small subsets
Bela Bollobas, Imre Leader, Marius Tiba
In this paper we start to investigate a new body of questions in additive combinatorics. The fundamental Cauchy--Davenport theorem gives a lower bound on the size of a sumset A+B f…
A strengthening of Freiman's 3k-4 theorem
Bela Bollobas, Imre Leader, Marius Tiba
In its usual form, Freiman's 3k-4 theorem states that if A and B are subsets of the integers of size k with small sumset (of size close to 2k) then they are very close to arithmeti…
Counting independent sets in regular hypergraphs
Jozsef Balogh, Bela Bollobas, Bhargav Narayanan
Amongst -regular -uniform hypergraphs on vertices, which ones have the largest number of independent sets? While the analogous problem for graphs (originally raised by Gr…
Topological Phase Transitions in Spatial Networks
Paul Balister, Chaoming Song, Oliver Riordan +2
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each o…
Dense Subgraphs in Random Graphs
Paul Balister, Béla Bollobás, Julian Sahasrabudhe +1
For a constant and a graph , let be the largest integer for which there exists a -vertex subgraph of with at least edges. We show…