Edge choosability of planar graphs without 5-cycles with a chord

Let G be a plane graph having no 5-cycles with a chord. If either Δ ≥ 6 , or Δ = 5 and G contains no 4-cycles with a chord or no 6-cycles with a chord, then G is edge- ( Δ + 1 ) -choosable, where Δ denotes the maximum degree of G .