Graph Theory by Ronald Gould

Author:Ronald Gould
Language: eng
Format: epub, azw3
Publisher: DOVER PUBLICATIONS, INC.
Published: 2012-06-26T16:00:00+00:00

Chapter 6

Planarity

Section 6.1 Euler’s Formula

In Chapter 1 we introduced the puzzle of the three houses and the three utilities. The problem was to determine if we could connect each of the three utilities with each of the three houses so that none of the utility lines crossed. We attempted a drawing of the graph model K3, 3 in Figure 1.1.2. In this chapter we will show that no such drawing is possible in the plane.

A (p, q) graph G is said to be embeddable in the plane or planar if it is possible to draw G in the plane so that the edges of G intersect only at end vertices. If such a drawing has been done, we say that a plane embedding of the graph has been found.

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