6 papers · 1 filter
Rankings in directed configuration models with heavy tailed in-degrees
Xing Shi Cai, Pietro Caputo, Guillem Perarnau +1
We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degr…
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…
The -cut model in deterministic and random trees
Gabriel Berzunza, Xing Shi Cai, Cecilia Holmgren
The -cut number of rooted graphs was introduced by Cai et al. as a generalization of the classical cutting model by Meir and Moon. In this paper, we show that all moments of the…
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…
K-cut on paths and some trees
Xing Shi Cai, Luc Devroye, Cecilia Holmgren +1
We define the (random) -cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon except n…