Abstract
An edge-coloring of a graph G is equitable if, for each vertex v of G, the number of edges of any one color incident with v differs from the number of edges of any other color incident with v by at most one. In the paper, we prove that every 1-planar graph has an equitable edge-coloring with k colors for any integer \(k\ge 21\), and every planar graph has an equitable edge-coloring with k colors for any integer \(k\ge 12\).
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Acknowledgements
The authors are very grateful to the referees for their detailed suggestions and corrections which have greatly contributed to this final version. This work was partially supported by National Natural Science Foundation of China (11631014, 11271006).
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This work is supported by NSFC (11631014, 11271006) of China.
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Hu, DQ., Wu, JL., Yang, D. et al. On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs. Graphs and Combinatorics 33, 945–953 (2017). https://doi.org/10.1007/s00373-017-1786-3
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DOI: https://doi.org/10.1007/s00373-017-1786-3