TOTAL COLORINGS OF PLANAR GRAPHS WITH MAXIMUM DEGREE AT LEAST 7 AND WITHOUT ADJACENT 5-CYCLES
Xiang Tan · Bulletin of the Korean Mathematical Society · 2016
A k-total-coloring of a graph G is a coloring of using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number of G is the smallest integer k such that G has a k-total-coloring. Let G be a planar graph with maximum degree . In this paper, it`s proved that if and G does not contain adjacent 5-cycles, then the total chromatic number is .