Local structures in plane maps and distance colourings Original Research Article

A structural result on normal plane maps is presented. It strengthens a result by Borodin which is related to Kotzigʹs and Lebesgueʹs classical results. Then the t-distance chromatic number of a planar graph G with maximum degree Δ(G)⩽D where D⩾8 is proved to be bounded above by a polynomial in D of degree t−1.