3 papers
math.PR2020
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…
math.PR2020
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…
math.PR2018
Cutting resilient networks -- complete binary trees
Xing Shi Cai, Cecilia Holmgren
In our previous work, we introduced the random -cut number for rooted graphs. In this paper, we show that the distribution of the -cut number in complete binary trees of size…