Ian Payne, Department of Pure Mathematics, University of Waterloo
“Necessary Conditions for Graphs with Taylor Polymorphisms”
Even cycles with constants of length at least 6 are a class of graphs having no Taylor polymorphism. In trying to generalize this, I managed to show that the same holds for any bipartite graph of even girth (at least 8) with one additional magic property. Unfortunately for my ego, it turns out there is a nifty way to show that no bipartite graph with constants of girth greater than 4 can have a Taylor polymorphism. I will go through the interesting parts of the proof.