22 citations · 112 across the 37 of their papers we have counts for
4 papers · 1 filter
Percolation on random graphs with a fixed degree sequence
Nikolaos Fountoulakis, Felix Joos, Guillem Perarnau
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion…
Counting independent sets in cubic graphs of given girth
Guillem Perarnau, Will Perkins
We prove a tight upper bound on the independence polynomial (and total number of independent sets) of cubic graphs of girth at least 5. The bound is achieved by unions of the Heawo…
Local convergence and stability of tight bridge-addable graph classes
Guillaume Chapuy, Guillem Perarnau
A class of graphs is bridge-addable if given a graph in the class, any graph obtained by adding an edge between two connected components of is also in the class. The author…
How to determine if a random graph with a fixed degree sequence has a giant component
Felix Joos, Guillem Perarnau, Dieter Rautenbach +1
For a fixed degree sequence , let be a uniformly chosen (simple) graph on where the vertex has degree . In this p…