Unique-maximum edge-colouring of plane graphs with respect to faces
A unique-maximum k k -edge-colouring with respect to faces of a 2-edge-connected plane graph G G is an edge-colouring with colours 1,,k 1 ,  , k so that, for each face ? ? of G G , the maximum colour occurs exactly once on the edges of ? ? . We prove that any 2-edge-connected plane graph has such a colouring with 3 colours. If we require the colouring to be facially proper then 6 colours are enough.
edge-colouring plane graph unique-maximum colouring