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arXiv · 1801.08293

Finding induced subgraphs in scale-free inhomogeneous random graphs

Ellen Cardinaels·Johan S. H. van Leeuwaarden·Clara Stegehuis
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Abstract

We study the problem of finding a copy of a specific induced subgraph on inhomogeneous random graphs with infinite variance power-law degrees. We provide a fast algorithm that finds a copy of any connected graph $H$ on a fixed number of $k$ vertices as an induced subgraph in a random graph with $n$ vertices. By exploiting the scale-free graph structure, the algorithm runs in $O(n k)$ time for small values of $k$. As a corollary, this shows that the induced subgraph isomorphism problem can be solved in time $O(nk)$ for the inhomogeneous random graph. We test our algorithm on several real-world data sets.

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Ellen Cardinaels, Johan S. H. van Leeuwaarden, Clara Stegehuis. 2019-08-29. Finding induced subgraphs in scale-free inhomogeneous random graphs. https://doi.org/10.1007/978-3-319-92871-5_1

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