Coloring edges of embedded graphs
Journal of International Crisis and Risk Communication Research · 2000
In this paper, we prove that any graph G with maximum degree Delta > (*) over bar * (G) greater than or equal to (11+root 49-24 chi > (*) over bar *(Sigma))/2, which is embeddable in a surface Sigma of characteristic chi > (*) over bar *(Sigma) less than or equal to 1 and satisfies \V(G)\ > 2(Delta > (*) over bar * (G)-5)-2 root6+Delta > (*) over bar * (G), is class one, (C) 2000 John Wiley & Sons, Inc.