List-edge-colouring planar graphs with precoloured edges.

Let G be a simple planar graph of maximum degree Δ, let t be a positive integer, and let L be an edge list assignment on G with L(e)≥Δ+t for all e∈E(G). We prove that if H is a subgraph of G that has been L-edge-coloured, then the edge-precolouring can be extended to an L-edge-colouring of G, provided that H has maximum degree d≤t and either d≤t−4 or Δ is large enough (Δ≥16+d suffices). If d>t, there are examples for any choice of Δ where the extension is impossible.