@article{Bu2025, 
author = {Yuehua Bu and Hongrui Zheng and Hongguo Zhu},
title = {On the list injective coloring of planar graphs without a              4      −      -cycle intersecting with a              5      −      -cycle},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1814-1825},
keywords = {face, cycle, discharging method, planar graph, injective coloring},
url = {https://www.sciopen.com/article/10.3934/math.2025083},
doi = {10.3934/math.2025083},
abstract = {An injective coloring of a graph    G is a vertex coloring such that a pair of vertices obtain distinct colors if there is a path of length two between them. It is proved in this paper that        χ    i    l    (  G  )  ≤  Δ  +  4 if    Δ  ≥  12 when    G does not have a              4      −      -cycle intersecting with a              5      −      -cycle. Our result improves a previous result of Cai et al. in 2023, who showed that        χ    i    l    (  G  )  ≤  Δ  +  4 when    Δ  ≥  12 and    G has disjoint              5      −      -cycles.}
}