Weak degeneracy of line graphs of planar graphs

Weak degeneracy is a generalization of degeneracy introduced by Bernshteyn and Lee (2023) [1] as a natural upper bound of many coloring parameters of graphs. For a graph G, let chi(G), chi(& ell;)(G), chi(DP)(G), and wd(G) denote its chromatic number, list chromatic number, DP-chromatic number and weak degeneracy, respectively. It is known that chi(G)<=chi(& ell;)(G)<=chi DP(G)<= wd(G)+1. In this paper, we prove that if G is a planar graph with maximum degree Delta, then for its line graph L(G), we have (1) wd(L(G))=Delta-1, if Delta >= 21; (2) wd(L(G))<=Delta, if Delta >= 9. This extends some known results on list edge coloring and edge DP-coloring of planar graphs. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.