# Noon lecture

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On 11.08.2011 at 12:20 in S11, there is the following noon lecture:

# Distribution of certain types of spanning subgraphs in G(n,p)

## Jane Gao

## Abstract

The distributions of subgraphs with fixed sizes in various random graph models have been investigated by many authors. A general approach by Ruci\'{n}ski showed that the numbers of subgraphs with fixed sizes in the binomial model $G(n,p)$ are asymptotically normal for a large range of $p$. However, the distributions of subgraphs with growing sizes, for instance, the spanning subgraphs, behave significantly differently.

In this work we describe a general approach of determining the distribution of the number of spanning subgraphs in the random graph $G(n,p)$. In particular, we determine the distribution of the number of $d$-factors, of spanning triangle-free subgraphs, of Hamilton cycles and of spanning subgraphs that are isomorphic to a collection of vertex disjoint triangles.

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