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Induced Subgraphs in Sparse Random Graphs with Given Degree Sequence

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Gao,  Pu
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:1011.3810.pdf
(Preprint), 307KB

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Citation

Gao, P., Su, Y., & Wormald, N. (2010). Induced Subgraphs in Sparse Random Graphs with Given Degree Sequence. Retrieved from http://arxiv.org/abs/1011.3810.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0019-DBFD-4
Abstract
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{{\bf d}}$, the probability space of random graphs with a given degree sequence $\bf d$.