Seminar Details
Triangle-Intersecting Families of Graphs
- Start Date: November 11, 2020
- Event Start Time: 12:15 PM
- Event End Time: 1:15 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Rashmika Goswami - Rutgers University
- Event Location: Online Event
- Event Additional Info: <p>Presented via Zoom - Meeting ID: 984 4140 9199</p> <p><a href="https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Frutgers.zoom.us%2Fj%2F98441409199&data=02%7C01%7C%7Cd0dafeb4d9624685e3db08d85a3f79f1%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C637358575952517368&sdata=eIii%2BsVwtvrWDLVmoAyel21mUBUrXe%2BQlrWkRm349Gc%3D&reserved=0">https://rutgers.zoom.us/j/98441409199</a></p> <p>Password: 715004</p> <p> </p>
- Presentation Type: Stand Alone Presentation
- 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.