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Adjacent vertex distinguishing edge coloring of IC-planar graphs

Abstract

The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring in which each pair of adjacent vertices is assigned different color sets. The smallest number of colors for which G has such a coloring is denoted by \(\chi '_a(G)\). An important conjecture due to Zhang et al. (Appl Math Lett 15:623–626, 2002) asserts that \(\chi '_a(G)\le \Delta (G)+2\) for any connected graph G with order at least 6. By applying the discharging method, we show that this conjecture is true for any IC-planar graph G with \(\Delta (G)\ge 16\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (12071260, 12001154), and the Natural Science Foundation of Hebei Province(A2021202025).

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Correspondence to Changqing Xu.

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Liu, Z., Xu, C. Adjacent vertex distinguishing edge coloring of IC-planar graphs. J Comb Optim (2021). https://doi.org/10.1007/s10878-021-00807-0

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Keywords

  • IC-planar graph
  • Adjacent vertex distinguishing edge coloring
  • Discharging method