Poisson approximation of induced subgraph counts in an inhomogeneous random intersection graph model
Bull. Korean Math. Soc.
Published online July 18, 2019
Yilun Shang
Northumbria University
Abstract : In this paper, we consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices $n$ and the number of elements $m$, scaling as $m=\lfloor\beta n^{\alpha}\rfloor$ $(\alpha,\beta>0)$, tend to infinity.
Keywords : Poisson approximation, Stein's method, Random graph, intersection graph
MSC numbers : 60F05 05C80 62E17
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd