3 papers
math.PR2026
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 ErdÅs--Rényi process, due to the dependence between edges added at different…
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 in the random graph , focusing on the case when . Our main results capture the 'leading term…
math.PR2025
The phase transition in bounded-size Achlioptas processes
Oliver Riordan, Lutz Warnke
Perhaps the best understood phase transition is that in the component structure of the uniform random graph process introduced by ErdÅs and Rényi around 1960. Since the model is…