A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory by Miklós Bóna
Author:Miklós Bóna
Language: eng
Format: epub
ISBN: 9789813148864
Publisher: World Scientific Publishing Co. Pte. Ltd.
Published: 2017-03-18T04:00:00+00:00
Chapter 12
Do Not Cross. Planar Graphs
12.1 Euler’s Theorem for Planar Graphs
Let us assume that a farming community has three houses and three wells. The families living in the three houses cannot stand each other, so they prefer not to meet when they walk to the wells. Can we build roads from each of the houses to each of the wells so that there will be no two roads among the needed nine roads that intersect? We are not allowed to build bridges or tunnels.
Figure 12.1 shows a credible, but failed, attempt to build such roads.
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