The ACO Seminar (2015–2016)

Polarity graphs coming from projective planes have an intimate connection with the extremal number for the 4-cycle. We will discuss finding a dense subgraph of a polarity graph and its relationship to the parameter ex(n, C₄). In addition, motivated by some questions of Mubayi and Williford, we will discuss the chromatic and independence numbers of various polarity graphs. This is joint work with Sam Peng and Craig Timmons.