Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World
Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World
3rd Edition
ISBN: 9781259232848
Author: David Sobecki, Allan Bluman
Publisher: McGraw-Hill Education
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Chapter 14.1, Problem 43E

In Exercises 43–50, use graph coloring to find the smallest number of colors needed to color the map so that no regions sharing a common border are the same color.

43.    Chapter 14.1, Problem 43E, In Exercises 4350, use graph coloring to find the smallest number of colors needed to color the map

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Chapter 14 Solutions

Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World

Ch. 14.1 - Draw a graph to represent ferry service between...Ch. 14.1 - The floor plan shown in Figure 14-7 is for a...Ch. 14.1 - Prob. 3TTOCh. 14.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 14.1 - Prob. 5TTOCh. 14.1 - Prob. 6TTOCh. 14.1 - Prob. 7TTOCh. 14.1 - Prob. 8TTOCh. 14.1 - Prob. 1ECh. 14.1 - What is the difference between a loop and a...
Ch. 14.1 - What is the difference between a circuit and a...Ch. 14.1 - Draw two graphs that look physically different but...Ch. 14.1 - Prob. 5ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - How does graph coloring apply to maps?Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 18ECh. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 20ECh. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - For Exercises 3134, represent each figure using a...Ch. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - For Exercises 3538, draw a graph to represent each...Ch. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - For Exercises 3942, draw a graph that represents...Ch. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - In Exercises 4350, use graph coloring to find the...Ch. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - In Exercises 4350, use graph coloring to find the...Ch. 14.1 - Prob. 48ECh. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Draw a graph that represents the street map in...Ch. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - (a)When a graph represents a map as in Exercise...Ch. 14.2 - Use Eulers theorem to determine if the graphs...Ch. 14.2 - Prob. 2TTOCh. 14.2 - Prob. 3TTOCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - For Exercises 710, decide whether each connected...Ch. 14.2 - Prob. 8ECh. 14.2 - For Exercises 710, decide whether each connected...Ch. 14.2 - Prob. 10ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 12ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 14ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 16ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 18ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - For Exercises 2126, draw a graph for the figures...Ch. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - For Exercises 33 and 34, determine if an Euler...Ch. 14.2 - For Exercises 33 and 34, determine if an Euler...Ch. 14.2 - Prob. 35ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - Draw some sample graphs and use them to discuss...Ch. 14.2 - Prob. 40ECh. 14.2 - Prob. 41ECh. 14.2 - Prob. 42ECh. 14.2 - Explain why the word connected is crucial...Ch. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.3 - Find a Hamilton path that begins at vertex C for...Ch. 14.3 - Prob. 2TTOCh. 14.3 - Prob. 3TTOCh. 14.3 - The driving times in minutes between four cities...Ch. 14.3 - Prob. 5TTOCh. 14.3 - Prob. 6TTOCh. 14.3 - Prob. 7TTOCh. 14.3 - What is the difference between a Hamilton path and...Ch. 14.3 - Prob. 2ECh. 14.3 - Give an example of a problem in our world that can...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Describe what a typical traveling salesperson...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 20ECh. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - For Exercises 1924, find two different Hamilton...Ch. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - For Exercises 2528, find the number of Hamilton...Ch. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - For Exercises 29 and 30, use the brute force...Ch. 14.3 - For Exercises 3134, use the nearest neighbor...Ch. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - In Exercises 3538, use the cheapest link algorithm...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - For Exercises 3942, use the information in the...Ch. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - For Exercises 4346, use the information in the...Ch. 14.3 - For Exercises 4346, use the information in the...Ch. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - A pizza delivery person has five prearranged...Ch. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.3 - Prob. 51ECh. 14.3 - Prob. 52ECh. 14.3 - When planning routes, distance isnt always the key...Ch. 14.3 - Prob. 54ECh. 14.3 - Repeat questions 51 through 54, choosing four...Ch. 14.3 - Prob. 56ECh. 14.3 - Prob. 57ECh. 14.3 - Prob. 58ECh. 14.3 - Find a road atlas that has a mileage chart. Pick...Ch. 14.3 - Prob. 60ECh. 14.3 - Prob. 61ECh. 14.3 - Prob. 62ECh. 14.3 - Prob. 63ECh. 14.3 - Prob. 64ECh. 14.3 - Prob. 65ECh. 14.3 - Prob. 66ECh. 14.4 - Prob. 1TTOCh. 14.4 - Prob. 2TTOCh. 14.4 - Prob. 3TTOCh. 14.4 - Prob. 4TTOCh. 14.4 - Prob. 5TTOCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - For Exercise 716, decide whether or not each graph...Ch. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - As a new suburban neighborhood is being built, the...Ch. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - In the last two sections, we used both Hamilton...Ch. 14.4 - Prob. 41ECh. 14.4 - Prob. 42ECh. 14 - Use the graph shown in Figure 14-62 for Exercise...Ch. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Use the graph shown in Figure 14-62 for Exercises...Ch. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Repeat Exercise 13 for the graphs from Exercises...Ch. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - For the following graph: (a)What is the degree of...Ch. 14 - Draw a graph with two bridges, and the...Ch. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - (a)For the graph shown in Figure 14-73, find an...Ch. 14 - Prob. 6CTCh. 14 - For the housing plan shown in Figure 14-75, draw a...Ch. 14 - Prob. 8CTCh. 14 - Use the brute force method to find the shortest...Ch. 14 - Use the nearest neighbor method and cheapest link...Ch. 14 - Prob. 11CTCh. 14 - Decide whether the problem can be solved using...
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