Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Subgraph densities in signed graphons and the local Simonovits-Sidorenko conjecture.
The asymptotic behavior of elementary symmetric functions on a probability distribution.
The block connectivity of random trees.
The Chromatic Number of Random Intersection Graphs
We study problems related to the chromatic number of a random intersection graph G (n,m, p). We introduce two new algorithms which colour G (n,m, p) with almost optimum number of colours with probability tending to 1 as n → ∞. Moreover we find a range of parameters for which the chromatic number of G (n,m, p) asymptotically equals its clique number.
The evolution of uniform random planar graphs.
The independent domination number of a random graph
We prove a two-point concentration for the independent domination number of the random graph provided p²ln(n) ≥ 64ln((lnn)/p).
The largest component in an inhomogeneous random intersection graph with clustering.
The lower tail of the random minimum spanning tree.
The Markov chain asymptotics of random mapping graphs
The outer-distance of nodes in random trees.
The permutation group induced on a moiety.
The sizes of components in random circle graphs
We study random circle graphs which are generated by throwing n points (vertices) on the circle of unit circumference at random and joining them by an edge if the length of shorter arc between them is less than or equal to a given parameter d. We derive here some exact and asymptotic results on sizes (the numbers of vertices) of "typical" connected components for different ways of sampling them. By studying the joint distribution of the sizes of two components, we "go into" the structure of random...
The spectral gap of random graphs with given expected degrees.
The -stability number of a random graph.
The two uniform infinite quadrangulations of the plane have the same law
We prove that the uniform infinite random quadrangulations defined respectively by Chassaing–Durhuus and Krikun have the same distribution.
Threshold functions for the bipartite Turán property.
Upper bounds on the non-3-colourability threshold of random graphs.
Using Lovász local lemma in the space of random injections.
Using R to Build and Assess Network Models in Biology
In this paper we build and analyze networks using the statistical and programming environment R and the igraph package. We investigate random, small-world, and scale-free networks and test a standard problem of connectivity on a random graph. We then develop a method to study how vaccination can alter the structure of a disease transmission network. We also discuss a variety of other uses for networks in biology.