Rashmika Goswami, Rutgers University

Abstract

We say a family of graphs is triangle-intersecting if the intersection of any two graphs in the family contains a triangle. If we consider graphs on n vertices, how large can such a family be? It is clear that we can get 1/8 of the graphs by fixing a triangle and taking all of the graphs containing that triangle - such a family is called a Δumvirate. In fact, as Ellis, Filmus, and Friedgut showed in 2012, this is the best we can do: not only is such a family the unique extremal example, it is also stable in the sense that any family with size close to the upper bound is close to a Δumvirate. I will go over this proof, which uses an interesting combination of techniques from different areas of combinatorics.

Presented via Zoom - Meeting ID: 984 4140 9199

https://rutgers.zoom.us/j/98441409199

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