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.
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Polyhedra without Coloring | Vertex Coloring | Edge Coloring |
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