| 1-Planar Graphs with Girth at Least 7 are $(1,1,1,0)$-Colorable |
| Received:March 28, 2016 Revised:May 30, 2016 |
| Key Words:
1-planar improper coloring discharging important 4-vertex
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11271365) and the Joint Funds of Department of Education under the Natural Science Funds of Shandong Province (Grant No.ZR2014JL001). |
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| Abstract: |
| 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, it is shown that 1-planar graphs with girth at least 7 are $(1,1,1,0)$-colorable. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.06.002 |
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