1-Planar Graphs with Girth at Least 7 are $(1,1,1,0)$-Colorable
Received:March 28, 2016  Revised:May 30, 2016
Key Word: 1-planar   improper coloring   discharging   important 4-vertex  
Fund ProjectL: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).
Author NameAffiliation
Ya-nan CHU School of Mathematics and Statistics, Shandong Normal University, Shandong 250014, P. R. China 
Lei SUN School of Mathematics and Statistics, Shandong Normal University, Shandong 250014, P. R. China 
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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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