Graph Family Operations|
Abstract: Paul Catlin introduced four functions, S^O, S^R, S^C, and S^H acting on a set S to produce another set. These functions have proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero k-flows for a fixed integer k \ge 3. In this talk (based on a paper by Catlin, Hobbs, and H.-J. Lai), we explore the relations between these functions, showing that there is a sort of duality between them and that they act as inverses of one another on certain sets of graphs.