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, we confirm the total-coloring conjecture for 1-planar graphs with maximum degree at least 13.
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Acknowledgments
This research is mainly supported by the Fundamental Research Funds for the Central Universities (No. K5051370003) and the Natural Science Basic Research Plan in Shaanxi Province of China (project title: On the structural properties and colorings of some classes of topological graphs), and is partially supported by the NSFC Grants 11001055, 11101243, 11201440, 61070230 and the NSFFP grant 2011J06001.
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Zhang, X., Hou, J. & Liu, G. On total colorings of 1-planar graphs. J Comb Optim 30, 160–173 (2015). https://doi.org/10.1007/s10878-013-9641-9
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DOI: https://doi.org/10.1007/s10878-013-9641-9