##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Fan Chung

#### UCSD

## From random graphs to graph limits and graphlets

##### Abstract:

We will discuss recent developments in the probabilistic and spectral approaches for graph limits. In particular, we will extend the notion of quasi-randomness, which concerns a class of equivalent properties that random graphs satisfy. For example, we will give several necessary and sufficient conditions for a graph to be the union of two or more quasi-random graphs. One of these characterizations involves eigenvalues and scalable eigenspaces, that we call "graphslets", which dictate the behavior of graph limits for both dense and sparse graphs.

### May 8, 2012

### 4:00 PM

### AP&M 7321

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