Finding Delta(Sigma) for a Surface Sigma of Characteristic chi(Sigma) =-5

For each surface Sigma, we define Delta(Sigma)= max{Delta(G)|G is a class two graph of maximum degree Delta(G) that can be embedded in Sigma}. Hence, Vizing\u27s Planar Graph Conjecture can be restated as Delta(Sigma) = 5 if Sigma is a plane. In this paper, we show that Delta(Sigma)= 9 if Sigma is a surface of characteristic chi(Sigma) = -5. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 148-168, 201