Few Long Lists for Edge Choosability of Planar Cubic Graphs
  It is known that every loopless cubic graph is 4-edge choosable. We prove the following strengthened result.   Let G be a planar cubic graph having b cut-edges. There exists a set F of at most 5b/2 edges of G with the following property. For any function L which assigns to each edge of F a set of 4 colours and which assigns to each edge in E(G)-F a set of 3 colours, the graph G has a proper edge colouring where the colour of each edge e belongs to L(e). 
Luis Goddyn and Andrea Spencer
math.CO