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[A graph is said to be embedded in the plane if it can be drawn on the plane so that no two edges intersect. Such a graph is called a planar graph. Graphs arising from maps are clearly planar. In fact, planar maps can be characterized as such. Any planar map cuts out the plane into faces. To be precise, a maximal region of the plane which does not contain in its interior a vertex of the graph is called a face. A finite plane graph has also one unbounded face called the outer face. The faces are pairwise disjoint. The basic relation for planar graphs is the following theorem due to Euler.]
Published: May 24, 2017
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