### Unavoidable dense induced subgraphs

- Series
- Graph Theory Seminar
- Time
- Tuesday, September 8, 2020 - 15:45 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/681348075/???? (replace ???? with password). For password, please email Anton Bernshteyn (bahtoh~at~gatech.edu)
- Speaker
- Rose McCarty – University of Waterloo – rose.mccarty@uwaterloo.ca

Thomassen conjectures that every graph of sufficiently large average degree has a subgraph of average degree at least d and girth at least k, for any d and k. What if we want the subgraph to be induced? Large cliques and bicliques are the obvious obstructions; we conjecture there are no others. We survey results in this direction, and we prove that every bipartite graph of sufficiently large average degree has either K_{d,d} or an induced subgraph of average degree at least d and girth at least 6.