Simultaneously Colouring the Edges and Faces of Plane Graphs

@article{Waller1997SimultaneouslyCT,
  title={Simultaneously Colouring the Edges and Faces of Plane Graphs},
  author={Adrian O. Waller},
  journal={J. Comb. Theory, Ser. B},
  year={1997},
  volume={69},
  pages={219-221}
}
The elements of a plane graph G are the edges, vertices, and faces of G. We say that two elements are neighbours in G if they are incident with or are mutually adjacent with each other in G. The simultaneous colouring of distinct elements of a planar graph was first introduced by Ringel [12]. In his paper Ringel considered the problem of colouring the vertices and faces of a plane graph in such a way that every vertex and face receives a different colour from any of its neighbouring vertices… CONTINUE READING

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