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\textsc{N16}
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\textsc{Colloquium}
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\textit{Random Subgraphs of a Given Graph}
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Paul Horn\par
The University of California, San Diego
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\textbf{Abstract:} Data from real-world graphs often contains incomplete information,
so we only observe subgraphs of these graphs. It is therefore
desirable to understand how a typical subgraph relates to the
underlying host graph.

We consider several interrelated problems involving both random trees
in host graphs and random subgraphs obtained by taking edges of the
host graph independently with probability p. In the second case,
we study the emergence of the giant component. We also use the
spectral gap to understand discrepancy and expansion properties
of a random subgraph.

The Erdos-Renyi random graph is the special case of this where the
host graph is the complete graph Kn. Additional applications include
taking a contact graph as the host graph, and viewing random subgraphs
as outbreaks of a disease.\vspace{\fill}
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Thursday, February 19, 2009, 3:00 pm\par
Mathematics and Science Center: W303
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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