Abstract
A graph $$G$$G is edge-$$L$$L-colorable if for a given edge assignment $$L=\{L(e):e\in E(G)\}$$L={L(e):e?E(G)}, there exits a proper edge-coloring $$\phi $$? of $$G$$G such that $$\phi (e)\in L(e)$$?(e)?L(e) for all $$e\in E(G)$$e?E(G). If $$G$$G is edge-$$L$$L-colorable for every edge assignment $$L$$L with $$| L(e)|\ge k$$|L(e)|?k for $$e\in E(G)$$e?E(G), then $$G$$G is said to be edge-$$k$$k-choosable. In this paper, we prove that if $$G$$G is a planar graph without non-induced $$6$$6-cycles, then $$G$$G is edge-$$k$$k-choosable, where $$k=\max \{8, \Delta (G)+1\}$$k=max{8,Δ(G)+1}.
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