Graphs that embedded in any fixed surfaces with sufficiently large maximum degree △ is total-(△

作者：Fang, Qiming^*; Zhang, Li^*

来源：AIMS Mathematics, 2024, 9(1): 1523-1534.

DOI：10.3934/math.2024075

• total coloring
• Euler characteristic
• surface
• maximum degree
• algebraic topology

Let G be a graph that can be embedded in a surface sigma of Euler characteristic c '(sigma). In this paper, we proved that there exists an integer increment 0 = 4 center dot (5 +root 49 - 24c ') center dot [2 - c ' + 21(5 +root 49 - 24c ')] such that the total chromatic number of G is increment (G) + 1 if increment (G) >= increment 0.

• 单位
  同济大学; 北京大学