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 ϕ of G such that ϕ ( 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 Δ ( G ) ≠ 5 and without adjacent 3-cycles, or with maximum degree Δ ( G ) ≠ 5 , 6 and without 7-cycles, then G is edge- ( Δ ( G ) + 1 ) -choosable.