Largest sparse subgraphs of random graphs.
For the Erdos-Rényi random graph Gn,p, we consider the order of a largest vertex subset that induces a subgraph with average degree at most t. For the case when both p and t are fixed, this value is asymptotically almost surely concentrated on at most two explicitly given points. This generalises a...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2011
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| Summary: | For the Erdos-Rényi random graph Gn,p, we consider the order of a largest vertex subset that induces a subgraph with average degree at most t. For the case when both p and t are fixed, 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. © 2011 Elsevier B.V. |
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