Largest sparse subgraphs of random graphs
For the Erdo{double acute}s-Rényi random graph G n,p, we give a precise asymptotic formula for the size α̂t(Gn,p) of a largest vertex subset in G n,p that induces a subgraph with average degree at most t, provided that p = p (n) is not too small and t = t (n) is not too large. In the case of fixed t...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2014
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| Summary: | For the Erdo{double acute}s-Rényi random graph G n,p, we give a precise asymptotic formula for the size α̂t(Gn,p) of a largest vertex subset in G n,p that induces a subgraph with average degree at most t, provided that p = p (n) is not too small and t = t (n) is not too large. In the case of fixed t and p, we find that this value is asymptotically almost surely concentrated on at most two explicitly given points. This generalises a result on the independence number of random graphs. For both the upper and lower bounds, we rely on large deviations inequalities for the binomial distribution. © 2013 Elsevier Ltd. |
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