Abstract
Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 8 and G is free of k-cycles for some k ∈ {5,6}, then the total chromatic number χ′′(G) of G is Δ + 1.
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This work is supported by a research grant NSFC(60673047) and SRFDP(20040422004) of China.
Received: February 27, 2007. Final version received: December 12, 2007.
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Hou, J., Zhu, Y., Liu, G. et al. Total Colorings of Planar Graphs without Small Cycles. Graphs and Combinatorics 24, 91–100 (2008). https://doi.org/10.1007/s00373-008-0778-8
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DOI: https://doi.org/10.1007/s00373-008-0778-8