Edge-choosability of planar graphs without adjacent triangles or without 7-cycles

A graph GG is edge-LL-colorable, if for a given edge assignment L={L(e):e∈E(G)}L={L(e):e∈E(G)}, there exists a proper edge-coloring ϕϕ of GG such that ϕ(e)∈L(e)ϕ(e)∈L(e) for all e∈E(G)e∈E(G). If GG is edge-LL-colorable for every edge assignment LL with |L(e)|≥k|L(e)|≥k for e∈E(G)e∈E(G), then GG is said to be edge-kk-choosable. In this paper, we prove that if GG is a planar graph with maximum degree Δ(G)≠5Δ(G)≠5 and without adjacent 3-cycles, or with maximum degree Δ(G)≠5,6Δ(G)≠5,6 and without 7-cycles, then GG is edge-(Δ(G)+1)(Δ(G)+1)-choosable.