MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
9th Edition
ISBN: 9780136415893
Author: Tannenbaum
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Chapter 6, Problem 67E

Complete bipartite graphs. A complete bipartite graph is a graph with the property that the vertices can be divided into two sets A and B and each vertex in a set A is adjacent to each of the vertices in set B . There are no other edges! If there are m vertices in set A and n vertices in set B, the complete bipartite graph is written as K m , n . F i g u r e 6 - 5 2 shows a generic bipartite graph.

Chapter 6, Problem 67E, Complete bipartite graphs. A complete bipartite graph is a graph with the property that the vertices

F i g u r e 6 - 5 2

a. For n > 1 , the complete bipartite graphs of the form K n , n all have Hamilton circuits. Explain why.

b. If the difference between m and n is exactly 1 ( i .e .,  | m n | = 1 ) , the complete bipartite graph K m , n has Hamilton path. Explain why.

c. When the difference between m and n is more than 1, then the complete bipartite graph K m , n has neither a Hamilton circuit nor a Hamilton path. Explain why.

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Chapter 6 Solutions

MYLAB MATH FOR EXCURSIONS IN MATHEMATIC

Ch. 6 - Consider the graph in Fig.6-27. a. Find all the...Ch. 6 - Prob. 12ECh. 6 - For the graph in Fig.6-29 a. find a Hamilton path...Ch. 6 - For the graph in Fig.6-30 a. find a Hamilton path...Ch. 6 - Explain why the graph shown in Fig.6-31 has...Ch. 6 - Explain why the graph shown in Fig.6-32 has...Ch. 6 - For the weighted shown in Fig 6-33, a.find the...Ch. 6 - For the weighted graph shown in Fig6-34, a.find...Ch. 6 - For the weighted graph shown in Fig6-35, a.find a...Ch. 6 - For the weighted graph shown in Fig6-36, a.find a...Ch. 6 - Suppose you have a supercomputer that can generate...Ch. 6 - Suppose you have a supercomputer that can generate...Ch. 6 - Prob. 23ECh. 6 - a. How many edges are there in K200? b. How many...Ch. 6 - In each case, find the value of N. a. KN has 120...Ch. 6 - In each case, find the value of N. a. KN has 720...Ch. 6 - Find an optimal tour for the TSP given in...Ch. 6 - Find an optimal tour for the TSP given in...Ch. 6 - A truck must deliver furniture to stores located...Ch. 6 - A social worker starts from her home A, must visit...Ch. 6 - You are planning to visit four cities A, B, C, and...Ch. 6 - An unmanned rover must be routed to visit four...Ch. 6 - For the weighted graph shown in Fig.6-41, i find...Ch. 6 - A delivery service must deliver packages at...Ch. 6 - Prob. 35ECh. 6 - A space mission is scheduled to visit the moons...Ch. 6 - This exercise refers to the furniture truck TSP...Ch. 6 - This exercise refers to the social worker TSP...Ch. 6 - Darren is a sales rep whose territory consists of...Ch. 6 - The Platonic Cowboys are a country and western...Ch. 6 - Find the repetitive nearest-neighbor tour and give...Ch. 6 - Prob. 42ECh. 6 - This exercise is a continuation of Darrens sales...Ch. 6 - This exercise is a continuation of the Platonic...Ch. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Find the cheapest-link tour and give its cost for...Ch. 6 - Find the cheapest-link tour for the social worker...Ch. 6 - For the Brute-Force Bandits concert tour discussed...Ch. 6 - For the weighted graph shown in Fig.6-47, find the...Ch. 6 - For Darrens sales trip problem discussed in...Ch. 6 - For the Platonic Cowboys concert tour discussed in...Ch. 6 - A rover on the planet Mercuria has to visit six...Ch. 6 - A robotic laser must drill holes on five sites A,...Ch. 6 - Prob. 55ECh. 6 - Prob. 56ECh. 6 - Suppose that in solving a TSP you find an...Ch. 6 - Prob. 58ECh. 6 - Prob. 59ECh. 6 - Prob. 60ECh. 6 - Prob. 61ECh. 6 - If the number of edges in K500 is x and the number...Ch. 6 - Explain why the cheapest edge in any graph is...Ch. 6 - a. Explain why the graph that has a bridge cannot...Ch. 6 - Julie is the marketing manager for a small...Ch. 6 - 66. m by n grid graphs. An m by n grid graph...Ch. 6 - Complete bipartite graphs. A complete bipartite...Ch. 6 - Prob. 68ECh. 6 - Diracs theorem. If G is a connected graph with N...
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