1. Using induction, prove that any planar graph can be colored in no more than 6 colors where no two vertices connected by an edge share the same color.

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(E.2) Answer the following question accordingly. Thanks in advance!
The following is a planar graph that can be drawn in the plane without any
edge crossings. We can evaluate not only the edges and vertices with the
given graph but also the faces (areas that are enclosed by edges)
3
Remember: If there are no areas enclosed by edges, as in a tree, we say
there is 1 face
Transcribed Image Text:The following is a planar graph that can be drawn in the plane without any edge crossings. We can evaluate not only the edges and vertices with the given graph but also the faces (areas that are enclosed by edges) 3 Remember: If there are no areas enclosed by edges, as in a tree, we say there is 1 face
1. Using induction, prove that any planar graph can be colored in no
more than 6 colors where no two vertices connected by an edge share the
same color.
Transcribed Image Text:1. Using induction, prove that any planar graph can be colored in no more than 6 colors where no two vertices connected by an edge share the same color.
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