Andrew Uzzell, 2017/05/26
Seminar series:  Colloquium
Presenter:Andrew Uzzell
Institution:University of Nebraska
Date:Friday, May 26th, 2017
Location:418 Machray Hall

Andrew Uzzell, 2017/05/26

Extremal graph theory is the study of optimization problems on families of graphs. Given a class of graphs $\mathcal{C}$ and a parameter $f$, what is the maximum (or minimum) value of $f$ over $\mathcal{C}$, and which members of $\mathcal{C}$ achieve the extreme value? Somewhat surprisingly, in many cases, such extremal results can both tell us how large $\mathcal{C}$ is and describethe typical structure of an element of $\mathcal{C}$.

The theory of graph limits, developed over the last dozen years by Lov\'asz and co-authors, provides an analytic framework for studying large graphs. We apply results due to Hatami, Janson, and Szegedy to determine the asymptotic size and typical structure of certain hereditary classes of graphs. We also prove analogous results for hereditary classes of so-called multicolored graphs. Our proofs combine counting arguments with analytic properties of the space of graph limits. This is joint work with Victor Falgas-Ravry, Svante Janson, and Johanna Stromberg.

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