Simultaneously colouring the edges and faces of plane graphs
In a simultaneous colouring of the edges and faces of the plane graph we colour edges and faces so that every two adjacent or incident pair of them receive different colours. In this paper we prove a conjecture of Mel'nikov which states that for this colouring every plane graph can be coloured with \(\Delta+3\) colours, where \(\Delta\) is the maximum degree of a vertex in the graph.
scientific article; zbMATH DE number 1006759
scientific article