Seminars & Colloquia Calendar
Triangle-Intersecting Families of Graphs
Rashmika Goswami, Rutgers University
Location: Zoom: please email: to be added to the mailing list
Date & time: Wednesday, 11 November 2020 at 12:15PM - 1:15PM
|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 ?umvirate. 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 ?umvirate. I will go over this proof, which uses an interesting combination of techniques from different areas of combinatorics.
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