To do a coloring for the vertices of a polyhedra, color the vertices so that no two vertices of the same color are connected by a common edge.
To do an edge coloring for a polyhedra, color the edges so that no two edges of the same color meet at a common vertex.
Each of these colorings must be done using the least number of colors
possible.
Consider the following example of vertex and edge colorings of
this polyhedra.
Polyhedra without Coloring | Vertex Coloring | Edge Coloring |
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