Adjacent vertex distinguishing edge coloring of IC-planar graphs

Zhuoya Liu and Changqing Xu ()
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Zhuoya Liu: Hebei University of Technology
Changqing Xu: Hebei University of Technology

Journal of Combinatorial Optimization, 2022, vol. 43, issue 4, No 2, 710-726

Abstract: 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 .

Keywords: IC-planar graph; Adjacent vertex distinguishing edge coloring; Discharging method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00807-0

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