BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.4, Problem 23ES

Textbook Problem

121 views

Scheduling Six different groups of children would like to visit the zoo and feed different animals. (Assume each group will visit the zoo on only one day.)

Group I would like to feed the bears, dolphins, and gorillas.

Group 2 would like to feed the bears, elephants, and hippos.

Group 3 would like to feed the dolphins and elephants.

Group 4 would like to feed the dolphins, zebras, and hippos.

Group 5 would like to feed the bears and hippos.

Group 6 would like to feed the gorillas, hippos, and zebras.

Use graph coloring to find the minimum number of days that are required so that all groups can feed the animals they would like to feed but no animals will be fed twice on the same day. Design a schedule to accomplish this goal.

To determine

The minimum number of days that all groups require to feed the animals.

**Given:**

Represent the information by a graph.

animals | Bears | Dolphins | Gorillas | Elephants | Hippos | Zebra |

Group1 | X | X | x | |||

Group2 | X | X | X | |||

Group3 | X | X | ||||

Group4 | X | X | X | |||

Group5 | X | X | ||||

Group 6 | X | X | X |

Mathematical Excursions (MindTap Course List)

Show all chapter solutions

Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...

Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Explain why the following two graphs cannot be...Ch. 5.1 - Label the vertices of the second graph so that it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Transportation For the train routes given in...Ch. 5.1 - Transportation For the direct air flights given in...Ch. 5.1 - Pets The diagram below shows the arrangement of a...Ch. 5.1 - Transportation A subway map is shown below. Is it...Ch. 5.1 - Architecture, a floor plan of a museum is shown....Ch. 5.1 - Architecture, a floor plan of a museum is shown....Ch. 5.1 - Degrees of Separation In the graph below, an edge...Ch. 5.1 - Social Network In the graph below, an edge...Ch. 5.1 - Bridges of a Graph An edge of a connected graph is...Ch. 5.1 - Travel A map of South America is shown at the...Ch. 5.2 - Continue investigating Hamiltonian circuits in...Ch. 5.2 - Use the greedy algorithm and the weighted graph...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Transportation For the train routes given in...Ch. 5.2 - Transportation For the direct air flights given in...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Travel A company representative lives in...Ch. 5.2 - Travel A tourist is staying in Toronto, Canada,...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Nicole wants to tour Asia. She will start...Ch. 5.2 - Travel The prices for traveling between five...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Route Planning Brian needs to visit the pet store,...Ch. 5.2 - Route Planning A bike messenger needs to deliver...Ch. 5.2 - Scheduling A research company has a large...Ch. 5.2 - Computer Networks A small office wishes to network...Ch. 5.2 - Route Planning A security officer patrolling a...Ch. 5.2 - Route Planning A city engineer needs to inspect...Ch. 5.2 - Draw a connected graph with six vertices that has...Ch. 5.2 - Assign weights to the edges of the following...Ch. 5.3 - The tetrahedron in figure 5.20 consists of four...Ch. 5.3 - The following graph is the projection of one ofthe...Ch. 5.3 - If we form a graph by a projection of the...Ch. 5.3 - Give a reason why the graph below Cannot be the...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the following graph contracts to K5.Ch. 5.3 - Show that the following graph contracts to the...Ch. 5.3 - Show that the graph is not planar by finding a...Ch. 5.3 - Show that the graph is not planar by finding a...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - If a planar drawing of a graph has 15 edges and 8...Ch. 5.3 - If a planar drawing of a graph has 100 vertices...Ch. 5.3 - Sketch a planar graph (without multiple edges or...Ch. 5.3 - Sketch a planar graph (without multiple edges or...Ch. 5.3 - Explain why it is not possible to draw a planar...Ch. 5.3 - If a planar drawing of a graph has twice as many...Ch. 5.3 - Show that the complete graph with five vertices,...Ch. 5.3 - Dual Graph Every planar graph has what is called a...Ch. 5.4 - A one-way road ends at a two-way street. The...Ch. 5.4 - A one-way road intersects a two-way road in a...Ch. 5.4 - A two-way road intersects another two-way road in...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Scheduling Six student clubs need to hold meetings...Ch. 5.4 - Scheduling Eight political committees must meet on...Ch. 5.4 - Scheduling Six different groups of children would...Ch. 5.4 - Scheduling Five different charity organizations...Ch. 5.4 - Scheduling Students in a film class have...Ch. 5.4 - Animal Housing A researcher has discovered six new...Ch. 5.4 - Wi-Fi Stations An office building is installing...Ch. 5.4 - Map Coloring Draw a map of a fictional continent...Ch. 5.4 - If the chromatic number of a graph with five...Ch. 5.4 - Edge Coloring In this section, we colored vertices...Ch. 5.4 - Scheduling Edge colorings, as explained in...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - Soccer In the table below, an X indicates teams...Ch. 5 - Each vertex in the graph at the left represents a...Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Parks The figure shows an arrangement of bridges...Ch. 5 - Architecture The floor plan of a sculpture gallery...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Travel The table below lists cities serviced by a...Ch. 5 - Travel For the direct flights given in Exercise...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Efficient Route The distances, in miles, between...Ch. 5 - Computer Networking A small office needs to...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graph is not planar.Ch. 5 - Show that the graph is not planar.Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Scheduling A company has scheduled a retreat at a...Ch. 5 - Social Network Each vertex in the graph at the...Ch. 5 - Determine whether the following two graphs are...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Recreation The illustration below depicts bridges...Ch. 5 - a. What does Dirac's theorem state? Explain how it...Ch. 5 - Low-Cost Route The table below shows the cost of...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Sketch a planar drawing of the graph below. Show...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Map Coloring A fictional map of the countries of a...Ch. 5 - For the graph shown below, find a 2-coloring of...Ch. 5 - A group of eight friends is planning a vacation in...

Find more solutions based on key concepts

Show solutions 71. Rental A rental truck costs for a day plus per mile.
If x is the number of miles driven, write an expressio...

Mathematical Applications for the Management, Life, and Social Sciences

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 6x(x2...

Finite Mathematics

Veterinary Science: Shetland Ponies How much should a healthy Shetland pony weigh? Let x be the age of the pony...

Understanding Basic Statistics

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 -6-13

Intermediate Algebra

Classify each function as a power function, root function, polynomial (state its degree), rational function, al...

Single Variable Calculus

In Exercises 516, evaluate the given quantity. log1/212

Finite Mathematics and Applied Calculus (MindTap Course List)

Find y by implicit differentiation. 35. x2 + 4y2 = 4

Single Variable Calculus: Early Transcendentals, Volume I

Maxwells equations relating the electric field E and magnetic field H as they vary with time in a region contai...

Calculus (MindTap Course List)

A test for the presence of a certain disease has probability .20 of giving a false-positive reading (indicating...

Probability and Statistics for Engineering and the Sciences

For each of the following sets of sample outcomes, use Formula 6.3 to construct the 99 confidence interval for ...

Essentials Of Statistics

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

Solving an Equation In Exercises 11-26, solve for x. 4x=64

Calculus: Early Transcendental Functions

Finding Limits Numerically In Exercises 5-12, complete the table and use the result to estimate the limit. Use ...

Calculus: An Applied Approach (MindTap Course List)

Find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

For each of the following, calculate the pooled variance and the estimated standard error for the sample mean d...

Statistics for The Behavioral Sciences (MindTap Course List)

(a) Make a large sketch of the curve described by the vector function r(t) = t2, t), 0 t 2, and draw the vect...

Calculus: Early Transcendentals

Graph the curve and find the area that it encloses. 16. r = 1 + 5 sin 6

Multivariable Calculus

Evaluating Composition of Functions Use f(x) = 2x 3 and g(x) = 4 x2 to evaluate the expression. 32. (a) (f f...

Precalculus: Mathematics for Calculus (Standalone Book)

Global Supply of Plutonium The global stockpile of plutonium for military applications between 1990 (t = 0) and...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Perform the indicated operation (write each result in scientific notation with the decimal part rounded to thre...

Elementary Technical Mathematics

22. Find the center for each of the following groups .
a. in Exercise 34 of section 3.1.
b. in Exercise 36 ...

Elements Of Modern Algebra

Round the following numbers to the indicated place. .44857 to hundredths

Contemporary Mathematics for Business & Consumers

In Exercises 1 to 8, find the perimeter of each polygon.

Elementary Geometry For College Students, 7e

Prove the third law of logarithms. [Hint: Start by showing that both sides of the equation have the same deriva...

Single Variable Calculus: Early Transcendentals

Evaluate each expression Without using a calculator. (Assume any variables represent positive numbers. sin(arcs...

Trigonometry (MindTap Course List)

A pair of dice is rolled, and the number that appears uppermost on each die is observed. In Exercises 1-6, refe...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding the Area of a Region In Exercises 11-14, (a) use a graphing utility to graph the region bounded by the ...

Calculus of a Single Variable

Gary and Carolyn plan to build the deck shown. a Find the total floor space area of the deck. b Find the approx...

Elementary Geometry for College Students

Think About It In Exercises 93-96, create a function whose graph has the given characteristics. (There is more ...

Calculus: Early Transcendental Functions (MindTap Course List)

Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Two s...

Mathematics For Machine Technology

Using Initial Conditions In Exercises 17-22, solve the differential equation by the method of undetermined coef...

Multivariable Calculus

Explain the purpose of a research proposal and how it differs from a research report.

Research Methods for the Behavioral Sciences (MindTap Course List)

How much work is done in lifting a 60-pound bag of bird seed 3 feet in the air?
20 ft-lbs
20g ft-lbs
180 ft-lbs...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let denote the me...

Introduction To Statistics And Data Analysis

Annual salary plus bonus data for chief executive officers are presented in the business-Week Annual Pay Survey...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Discovery and Writing In straight-line depreciation, explain why the slope of the line is called the rate of de...

College Algebra (MindTap Course List)

Which is true about the series ?
diverges
converges absolutely
converges conditionally
converges, but not absol...

Study Guide for Stewart's Multivariable Calculus, 8th

Determining Differentiability Where are the functions f1(x)=sinx and f2(x)=sinx differentiable?

Calculus (MindTap Course List)

Explain how an idea for a new research study can be obtained from an existing research publication and use exis...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends...

Statistics for Business & Economics, Revised (MindTap Course List)

In Exercises 87-90, use a trial-and-error process along with what you know about the digits used in a given bas...

Mathematics: A Practical Odyssey

Suppose a[1],a[2],a[3],....a[m] is a one-dimensional arry and consider the following algorithm segment: sum:=0f...

Discrete Mathematics With Applications

Using Technology In Exercises 51-56, use a graphing utility to graph the quadratic function. Find the x-interce...

College Algebra

Vehicle Quality Ratings. A J. D. Power and Associates vehicle quality survey asked new owners a variety of ques...

Essentials Of Statistics For Business & Economics

51. In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Secant Lines Find the equation of the secant line for the graph of y=x2+1fromx=2tox=3.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)