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math.CO2019
Counting extensions revisited
Matas Šileikis, Lutz Warnke
We consider rooted subgraphs in random graphs, i.e., extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three conn…
math.CO2019
A limit theorem for small cliques in inhomogeneous random graphs
Jan Hladky, Christos Pelekis, Matas Sileikis
The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erdős--Rényi random graph, called -random graphs. We prove, via…
math.PR2019
Upper tail bounds for Stars
Matas Šileikis, Lutz Warnke
For r \ge 2, let X be the number of r-armed stars K_{1,r} in the binomial random graph G_{n,p}. We study the upper tail \Pr(X \ge (1+ε)\E X), and establish exponential bounds which…