Abstract: While Turán type problems are the most studied topic in extremal combinatorics, some of the most basic bipartite degenerate Turán problems remain elusive. In this talk, I will discuss some recent progress on this topic and new results on bipartite graphs arising from geometric shapes and periodic tilings commonly found in nature, including even prisms, planar hexagonal tilings and quadrangulations of the plane, the cylinder and the torus.
This is joint work with Jun Gao, Oliver Janzer, and Zixiang Xu.
