Total coloring of embedded graphs with maximum degree at least seven

A k-total-coloring of a graph G is a coloring of V(G)@?E(G) using k colors such that no two adjacent or incident elements receive the same color. A graph G is k-total-colorable if it admits a k-total-coloring. In this paper, it is proved that any graph G which can be embedded in a surface @S of Euler characteristic @g(@S)>=0 is (@D(G)+2)-total-colorable if @D(G)>=7, where @D(G) denotes the maximum degree of G.