Bulletin of the Korean Mathematical Society (대한수학회보)

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LIST INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH AT LEAST FIVE

  • Hongyu Chen (School of Science Shanghai Institute of Technology)
  • Received : 2023.02.20
  • Accepted : 2023.11.28
  • Published : 2024.01.31
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Abstract

A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k-choosable if any list L of admissible colors on V (G) of size k allows an injective coloring 𝜑 such that 𝜑(v) ∈ L(v) whenever v ∈ V (G). The least k for which G is injectively k-choosable is denoted by χli(G). For a planar graph G, Bu et al. proved that χli(G) ≤ ∆ + 6 if girth g ≥ 5 and maximum degree ∆(G) ≥ 8. In this paper, we improve this result by showing that χli(G) ≤ ∆ + 6 for g ≥ 5 and arbitrary ∆(G).

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Acknowledgement

The author thanks the anonymous reviewers for their useful comments.

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