The number of connected graphs with a given sparse degree sequence is identified up to exponential order by viewing them as giant components in a suitably chosen configuration model and applying a switching argument.
Addario-Berry and G
2 Pith papers cite this work. Polarity classification is still indexing.
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In random graphs with feasible degree sequences containing a giant component, the giant is unique whp with explicit diameter and mixing-time bounds that are often tight, along with size and diameter controls on smaller components.
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The number and structure of connected graphs with a fixed degree sequence
The number of connected graphs with a given sparse degree sequence is identified up to exponential order by viewing them as giant components in a suitably chosen configuration model and applying a switching argument.
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Diameters and mixing times for giant components of random graphs with given degrees
In random graphs with feasible degree sequences containing a giant component, the giant is unique whp with explicit diameter and mixing-time bounds that are often tight, along with size and diameter controls on smaller components.