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Weak degeneracy of the square of planar graphs with given girth

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  • Ye, Jing
  • Han, Miaomiao
  • Xu, Murong

Abstract

Bernshteyn and Lee introduced weak degeneracy, showing that its value plus one bounds various graph coloring parameters. In this paper, we prove that if G is a planar graph with maximum degree Δ and girth g, then weak degeneracy wd(G2)=Δ holds independently under each of the following conditions: (i) Δ ≥ 16 and g=7; (ii) Δ ≥ 10 and 8 ≤ g ≤ 9; (iii) Δ ≥ 6 and 10 ≤ g ≤ 11; (iv) Δ=5 and g ≥ 12. This work generalizes the results obtained by Ivanova in [Journal of Applied and Industrial Mathematics, 5(2)(2011), 221–230].

Suggested Citation

  • Ye, Jing & Han, Miaomiao & Xu, Murong, 2026. "Weak degeneracy of the square of planar graphs with given girth," Applied Mathematics and Computation, Elsevier, vol. 517(C).
    • Handle: RePEc:eee:apmaco:v:517:y:2026:i:c:s0096300325006216
    DOI: 10.1016/j.amc.2025.129896
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    References listed on IDEAS

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    1. Ye, Jing & Zou, Jiani & Han, Miaomiao, 2025. "Weak degeneracy of the square of K4-minor free graphs," Applied Mathematics and Computation, Elsevier, vol. 500(C).
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