22 citations · 112 across the 37 of their papers we have counts for
4 papers · 1 filter
Minimum stationary values of sparse random directed graphs
Xing Shi Cai, Guillem Perarnau
We consider the stationary distribution of the simple random walk on the directed configuration model with bounded degrees. Provided that the minimum out-degree is at least , wi…
Two lower bounds for -centered colorings
Loïc Dubois, Gwenaël Joret, Guillem Perarnau +2
Given a graph and an integer , a coloring is \emph{-centered} if for every connected subgraph of , either uses more than colors o…
The giant component of the directed configuration model revisited
Xing Shi Cai, Guillem Perarnau
We prove a law of large numbers for the order and size of the largest strongly connected component in the directed configuration model. Our result extends previous work by Cooper a…
The diameter of the directed configuration model
Xing Shi Cai, Guillem Perarnau
We show that the diameter of the directed configuration model with vertices rescaled by converges in probability to a constant. Our assumptions are the convergence of…