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| A Totally(Δ+1)-colorable 1-planar Graph with Girth at Least Five | |
| 基金项目： | The second author is supported by National Natural Science Foundation of China (Grant No. 11271006) |
| 摘 要： | A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.In this paper,we prove that every 1-planar graph G with maximum degree Δ(G)≥12 and girth at least five is totally(Δ(G)+1)-colorable. |
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