嵌入曲面的特殊图的边染色

Edge Colourings of Embedded Special Graphs

设图G是嵌入到欧拉示性数χ(∑)≥0的曲面上的图,χ′(G)和△(G)分别表示图G的边色数和最大度.将证明如果G满足以下条件:1)△(G)≥5;2)图中3-圈和4-圈不相邻;3)图G中没有5-圈的一次剖分,则有χ′(G)=△(G).

Let G be a graph embedded on a surface of Euler characteristic χ（∑） ≥ 0. χ′（G） and △（G） denote the chromatic index and the maximum degree of G, respectively. The paper proves that χ′（G） = △（G） if the graph G with △（G） ≥ 5 satisfies the properties that there are no adjacent 3-cycles and 4-cycles in G and there is no subgraph isomorphic to one subdivision of 5-cycle in G.