Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3 - Page 924: 65

Answer

We can use a graph to model friendly relations between pairs of countries. Each vertex represents one country, and an edge between a pair of vertices shows that these two countries have friendly relations. The Hamilton circuit is B,E,D,C,F,A,B. This seating arrangement around the table will allow ambassadors to be seated between ambassadors from countries that have friendly relations with their own country.
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Work Step by Step

We can use a graph to model friendly relations between pairs of countries. Each vertex represents one country, and an edge between a pair of vertices shows that these two countries have friendly relations. We can use a Hamilton circuit to find a seating arrangement so that ambassadors are seated between ambassadors from countries that have friendly relations with their own country. We can start the Hamilton circuit with the vertices B, E. From vertex E, the path can travel to vertex D, then to vertex C, then to vertex F, then to vertex A, and finally back to vertex B. This path starts and ends at vertex B, and visits every other vertex exactly once. The Hamilton circuit is B,E,D,C,F,A,B. This seating arrangement around the table will allow ambassadors to be seated between ambassadors from countries that have friendly relations with their own country.
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