Möbius inversion and graph colorings

Nicholas Proudfoot, Department of Mathematics, University of Oregon

Abstract: A proper coloring of a graph is a way to label the vertices such that adjacent vertices get different labels. (The famous Four Color Theorem, proven in 1976, says that any graph that can be drawn on a blackboard without edge crossings admits at least one proper coloring with at most four different colors.) I'll discuss the beautiful theorem of Möbius inversion for functions on posets, and explain what it has to do with coloring graphs.