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Injective coloring of planar graphs with girth 5

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Abstract

A coloring of a graph G is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring. In this paper, we prove that for each planar graph with g ≥ 5 and Δ (G) ≥ 20, χi(G) ≤ Δ(G)+ 3.

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Acknowledgements

This paper was supported by the National Natural Science Foundation of China (No. 11771403).

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China

    Yuehua Bu & Piaopiao Ye

  2. Xingzhi College, Zhejiang Normal University, Jinhua, 321004, China

    Yuehua Bu

Authors
  1. Yuehua Bu
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  2. Piaopiao Ye
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Corresponding author

Correspondence to Yuehua Bu.

Additional information

Translated from Advances in Mathematics (China), 2018, 47(3): 363–372

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Bu, Y., Ye, P. Injective coloring of planar graphs with girth 5. Front. Math. China 17, 473–484 (2022). https://doi.org/10.1007/s11464-022-1018-x

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  • DOI: https://doi.org/10.1007/s11464-022-1018-x

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