====== Eric Swartz (Binghamton) ====== ====== Polygonal Graphs ====== ===== Abstract for the Combinatorics Seminar 2010 September 28 ===== A near-polygonal graph is a (simple) graph Γ which has a set //C// of cycles of length m, for some positive integer m, such that each 2-path of Γ is contained in exactly one cycle in //C//. If m is the girth of Γ then the graph is called polygonal. I will discuss basic results and recent progress, with a focus on a construction involving the derived graph of a voltage graph. ----