554 citations · 1.7k across the 51 of their papers we have counts for
58 papers
A short proof of the Erd\H os--Sós Conjecture
Oliver Riordan, Alex Scott
The Erd\H os--Sós Conjecture was recently proved by GPT-6 Astra, using a very ingenious and surprising argument. In this note, we present a simplified version of this argument in a…
Counting subgraphs in bounded-size Achlioptas processes
Mihyun Kang, Oliver Riordan
Achlioptas processes such as the Bohman--Frieze process are much harder to analyse than the classical Erdős--Rényi process, due to the dependence between edges added at different s…
Random cliques in random graphs revisited
Robert Morris, Oliver Riordan
We study the distribution of the set of copies of some given graph in the random graph , focusing on the case when . Our main results capture the 'leading term…
Thresholds and expectation thresholds for larger p
Tomasz Przybyłowski, Oliver Riordan
Let and be the threshold and the expectation threshold, respectively, of an increasing family of subsets of a finite set , and let $l…
How does the chromatic number of a random graph vary?
Annika Heckel, Oliver Riordan
How does the chromatic number of a graph chosen uniformly at random from all graphs on vertices behave? This quantity is a random variable, so one can ask (i) for upper and low…
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…