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arXiv · 1402.7242

Percolation with small clusters on random graphs

Mustazee Rahman
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Abstract

Consider the problem of determining the maximal induced subgraph in a random $d$-regular graph such that its components remain bounded as the size of the graph becomes arbitrarily large. We show, for asymptotically large $d$, that any such induced subgraph has size density at most $2(\log d)/d$ with high probability. A matching lower bound is known for independent sets. We also prove the analogous result for sparse Erd\H{o}s-R\'{e}nyi graphs.

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Mustazee Rahman. 2014-02-28. Percolation with small clusters on random graphs. https://doi.org/10.1007/s00373-015-1628-0

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