# Noon lecture

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On 22.12.2016 at 12:20 in S6, there is the following noon lecture:

# Concentration of extension counts in random graphs

## Matas Šileikis

## Abstract

A graph is epsilon-regular when the ratio of its maximum and minimum vertex degrees is at most 1 + epsilon. Given a fixed graph H, one can generalize the notion of regularity by replacing a vertex degree deg(v) by the number of copies of H containing vertex v (the vertex degrees correspond to the case H = K_2). In late 1980s Joel Spencer gave sufficient conditions for the random graph G(n,p) being epsilon-regular with respect to general H. I will present joint work with Lutz Warnke in which we study the sharpness of Spencer's results and refine them.

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