Gwen McKinley




Wednesday, December 7, 2022 - 2:00pm to 3:00pm


510R Rowland Hall

There is a rich and growing body of literature dedicated studying typical colorings, independent sets, and more general homomorphisms in regular bipartite graphs. Much of this literature has been devoted to the Hamming cube and the discrete torus, where very strong structural and enumerative results are known. However, a number of the techniques that have been used rely heavily on the specific structure of these graphs. Here, we consider the middle two layers of the Hamming cube, which have slightly less "nice structure" than the entire Hamming cube, and ask for the typical structure of a q-coloring (where q is any constant). When q is even, we prove analogous structural and enumerative results to those known for the Hamming cube. In this talk, I will discuss some of our techniques, and future directions to generalize this work to other graphs. This project is joint with Lina Li and Jinyoung Park.