The edge-coloring of graphs with small genus

Abstract

In this note, we prove that a graph is of class one if G can be embedded in a surface with positive characteristic and satisfies one of the following conditions: (i) Delta(G) greater than or equal to 3 and g(G) (the girth of G) greater than or equal to 8 (ii) Delta(G) greater than or equal to 4 and g(G) greater than or equal to 5; and (iii) Delta(G) greater than or equal to 5 and g(G) greater than or equal to 4.