15 citations · 18 across the 4 of their papers we have counts for
5 papers
Minors in random regular graphs
N. Fountoulakis, D. Kühn, D. Osthus
We show that there is a constant c>0 so that for any fixed r which is at least 3 a.a.s. an r-regular graph on n vertices contains a complete graph on c n^{1/2} vertices as a minor.…
The order of the largest complete minor in a random graph
N. Fountoulakis, D. Kühn, D. Osthus
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let G(n,p) denote a random graph on n vertices with edge prob…
Percolation on sparse random graphs with given degree sequence
Nikolaos Fountoulakis
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges…
The Evolution of the Mixing Rate
Nikolaos Fountoulakis, Bruce Reed
In this paper we present a study of the mixing time of a random walk on the largest component of a supercritical random graph, also known as the giant component. We identify local…
Embeddings and Ramsey numbers of sparse k-uniform hypergraphs
Oliver Cooley, Nikolaos Fountoulakis, Daniela Kühn +1
Chvatal, Roedl, Szemeredi and Trotter proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In previous work, we proved the same result for…