O. Riordan

activity

20042026

most citedThe phase transition in inhomogeneous random graphs

554 citations · 1.7k across the 51 of their papers we have counts for

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19 papers · 1 filter

math.CO2026

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…

math.CO2025

Random cliques in random graphs revisited

Robert Morris, Oliver Riordan

We study the distribution of the set of copies of some given graph $H$ in the random graph $G (n, p)$ , focusing on the case when $H = K_{r}$ . Our main results capture the 'leading term…

math.CO2023★ 2 cited

Thresholds and expectation thresholds for larger p

Tomasz Przybyłowski, Oliver Riordan

Let $p_{c}$ and $q_{c}$ be the threshold and the expectation threshold, respectively, of an increasing family $F$ of subsets of a finite set $X$ , and let $l…

math.CO2021★ 4 cited

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 $n$ vertices behave? This quantity is a random variable, so one can ask (i) for upper and low…

math.CO2018★ 1 cited

Random cliques in random graphs and sharp thresholds for $F$ -factors

Oliver Riordan

We show that for each $r \geq 4$ , in a density range extending up to, and slightly beyond, the threshold for a $K_{r}$ -factor, the copies of $K_{r}$ in the random graph $G (n, p)$ are rand…

math.CO2016

Counting racks of order n

Matthew Ashford, Oliver Riordan

A rack on $[n]$ can be thought of as a set of maps $(f_{x})_{x \in [n]}$ , where each $f_{x}$ is a permutation of $[n]$ such that $f_{(x) f_{y}} = f_{y}^{- 1} f_{x} f_{y}$ for all $x$ and $y$ . In 2…