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Adjacent vertex distinguishing edge coloring of IC-planar graphs

Author

Listed:
  • Zhuoya Liu

    (Hebei University of Technology)

  • Changqing Xu

    (Hebei University of Technology)

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 $$\chi '_a(G)$$ χ a ′ ( G ) . An important conjecture due to Zhang et al. (Appl Math Lett 15:623–626, 2002) asserts that $$\chi '_a(G)\le \Delta (G)+2$$ χ a ′ ( G ) ≤ Δ ( 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 $$\Delta (G)\ge 16$$ Δ ( G ) ≥ 16 .

Suggested Citation

  • Zhuoya Liu & Changqing Xu, 2022. "Adjacent vertex distinguishing edge coloring of IC-planar graphs," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 710-726, May.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:4:d:10.1007_s10878-021-00807-0
    DOI: 10.1007/s10878-021-00807-0
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    References listed on IDEAS

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    1. Hervé Hocquard & Mickaël Montassier, 2013. "Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 152-160, July.
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