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 Poisson approximation of induced subgraph counts in an inhomogeneous random intersection graph model Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1199-1210 https://doi.org/10.4134/BKMS.b180971Published online September 30, 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 : random graph, intersection graph, Poisson approximation, Stein's method, subgraph count MSC numbers : Primary 60F05, 05C80, 62E17 Downloads: Full-text PDF   Full-text HTML