2017/09/12 by Harrelson, Joshua, McDonald, Jessica, Puleo, Gregory J. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1709.04027
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.