3 papers
math.CO2025
The degree-restricted random process is far from uniform
Michael Molloy, Erlang Surya, Lutz Warnke
The degree-restricted random process is a natural algorithmic model for generating graphs with degree sequence D_n=(d_1, \ldots, d_n): starting with an empty n-vertex graph, it seq…
math.CO2025
Isomorphisms between dense random graphs
Erlang Surya, Lutz Warnke, Emily Zhu
We consider two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities p_1,p_2. In particular, (i) we prov…
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…