Normgraphs and multicolor Ramsey numbers
Tibor Szabo
University of Illinois at UrbanaChampaign
April 9,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Determining the maximum number of edges an $n$vertex simple graph can have
when it does NOT contain a fixed subgraph $H$ is one of the oldest and
moststudied problems of Extremal Graph Theory. The value is called the
{\it Tur\'an number} $ex(n;H)$. {\it Normgraphs} were introduced in a paper
by Koll\'ar, R\'onyai and the speaker to answer this question when $H$ is a
complete bipartite graph with appropriate partsizes.
In this talk we define normgraphs and discuss some variations
and generalizations of them. We obtain new sharp bounds for the
Tur\'an number of complete bipartite graphs. Applications in
Discrepancy Theory and Ramsey Theory will also be presented.
This talk presents joint work with Noga Alon and Lajos R\'onyai.

Speaker's Contact Info: tszabo(atsign)math.uiuc.edu
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