Face colorings of embedded graphs
D Archdeacon - Journal of graph theory, 1984 - Wiley Online Library
Journal of graph theory, 1984•Wiley Online Library
… We shall describe a single splitting to form a new graph S(G) which has minimum degree
at least 3 and is embedded on the same surface with a packed k-coloring of the faces. By
repeated application of this process, which necessarily terminates with a cubic … To
complete the proof of the converse, we start with the cubic splitting G' embedded on S with a
packed k-coloring of the faces. By a succession of edge contractions we can construct the
graph G embedded on S with a packed k-coloring of the faces. I …
at least 3 and is embedded on the same surface with a packed k-coloring of the faces. By
repeated application of this process, which necessarily terminates with a cubic … To
complete the proof of the converse, we start with the cubic splitting G' embedded on S with a
packed k-coloring of the faces. By a succession of edge contractions we can construct the
graph G embedded on S with a packed k-coloring of the faces. I …
Abstract
We characterize those graphs which have at least one embedding into some surface such that the faces can be properly colored in four or fewer colors. Embeddings into both orientable and nonorientable surfaces are considered.
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