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

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