We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erd¨os-R´enyi graph G(N, c/N) and r...
Finding the largest clique in random graphs is a well known hard problem. It is known that a random graph G(n, 1/2) almost surely has a clique of size about 2 log n. A simple greed...
Let k = (k1, . . . , kn) be a sequence of n integers. For an increasing monotone graph property P we say that a base graph G = ([n], E) is k-resilient with respect to P if for eve...
Sonny Ben-Shimon, Michael Krivelevich, Benny Sudak...
We show that nodes of high degree tend to occur infrequently in random graphs but frequently in a wide variety of graphs associated with real world search problems. We then study ...
Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random w...