BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.4, Problem 11ES

Textbook Problem

39 views

Show that the graph is 2-colorable by finding a 2-coloring. If the graph is not 2-colorable, explain why.

To determine

**To Prove:**

The given graph is not 2-colourable.

**Given information:**

The graph is

**Theorem used:**

__2-colourable theorem: __A graph is 2-colourable if and only if it has no circuits that consist of an odd number of vertices...

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 In Exercises 9-14, decide whether the specified values come from a linear, quadratic, exponential, or absolute ...

Finite Mathematics

In problems 5-8, Use a calculator to evaluate the indicated powers.
5.

Mathematical Applications for the Management, Life, and Social Sciences

Concept Quiz 2.1 For Problems 1-10, answer true or false. If the solution set is the null set, then the equatio...

Intermediate Algebra

SOC Data have been gathered on four variables for 15 respondents see the following table. Find and report the a...

Essentials Of Statistics

Convert the expressions in Exercises 31-36 to positive exponent form. 34x2/3

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 33. x2(4x2)3/2dx

Calculus: Early Transcendentals

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typi...

Single Variable Calculus: Early Transcendentals, Volume I

(a) What is an alternating series? (b) Under what conditions does an alternating series converge? (c) If these ...

Multivariable Calculus

Reconsider the minicomputer component lifetimes X and Y as described in Exercise 12. Determine E(XY). What can ...

Probability and Statistics for Engineering and the Sciences

In Exercises 3-6, simplify the expression. 12(3)x232x1/2

Calculus: An Applied Approach (MindTap Course List)

Baby Boomers and Medicare Benefits Aging baby boomers will put a strain on Medica benefits unless Congress take...

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

Expressing a Function as a Composition Express the function in the form f g. 66. G(x)=1x+3

Precalculus: Mathematics for Calculus (Standalone Book)

Is there a number a such that limx23x2+ax+a+3x2+x2 exists? If so, find the value of a and the value of the limi...

Single Variable Calculus

The distribution of scores on the SAT is approximately normal with a mean of Âµ = 500 and a standard deviation o...

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integral. 1+sinx1+cosxdx

Calculus (MindTap Course List)

IRS: Tax Returns Almost everyone files (or will someday file) a federal income tax return. A research poll for ...

Understanding Basic Statistics

Inverse Functions In Exercises 73-76, illustrate that the functions f and g are inverse functions of each other...

Calculus: Early Transcendental Functions

Solve each equation in Exercises 107120 for x, rounding your answer to four significant digits where necessary....

Applied Calculus

Participants enter a research study with unique characteristics that produce different scores from one person t...

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

Test for divisibility by 3 and check your result with a calculator: 178,213

Elementary Technical Mathematics

Prepare the following statements on separate sheets of paper.
Calculate the missing balance sheet items for Exe...

Contemporary Mathematics for Business & Consumers

y-intercept 6, parallel to the line 2x + 3y + 4 = 0

Single Variable Calculus: Early Transcendentals

Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the ver...

Trigonometry (MindTap Course List)

a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant polynomial in...

Elements Of Modern Algebra

For Exercises 48 and 49, use the formula found in Exercise 47. Find the area of a trapezoid with an altitude of...

Elementary Geometry For College Students, 7e

Change of Majors by students: Records compiled by the admissions office at a state university indicating the pe...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercise 1 to 10, classify each statement as true or false. CE=ED

Elementary Geometry for College Students

Finding Surface AreaIn Exercises 3-16, find the area of the surface given by z=f(x,y) that lies above the regio...

Calculus: Early Transcendental Functions (MindTap Course List)

Comparing Methods In Exercises 29 and 30, find the area of the region by integrating (a) with respect to x and ...

Calculus of a Single Variable

The volume of a regular pyramid with an equilateral triangle base is 3174 cubic centimeters. The pyramid height...

Mathematics For Machine Technology

If 4 is a critical number for f and fâ€²(x) < 0 for x < 4 and fâ€²(x) > 0 for x > 4, then:
f has a local maximum at...

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

Examining a Partial Derivative In Exercises 5-10, explain whether the Quotient Rule should he used to find the ...

Multivariable Calculus

Finding a Polar Equation In Exercises 119-122, find a polar equation for the conic with its focus at the pole a...

Calculus (MindTap Course List)

A spring with a 10-kg mass is immersed in a fluid with damping constant 60. To maintain the spring stretched 3 ...

Study Guide for Stewart's Multivariable Calculus, 8th

Describe how some behaviors can be explained by clichÃ©s, such as â€œYou cant teach an old dog new tricks or â€œYou ...

Research Methods for the Behavioral Sciences (MindTap Course List)

For each of the following operational definitions, decide whether you consider it to be a valid measure. Explai...

Research Methods for the Behavioral Sciences (MindTap Course List)

Containers A box has a length of 16 inches, width of 10 inches, and a height of between 4 inches and 8 inches. ...

College Algebra (MindTap Course List)

In Table 15.12 we provided estimates of the probability of using the coupon in the Simmons Stores catalog promo...

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

Peak force (N) on the hand was measured just prior to impact and just after impact on a backhand drive for six ...

Introduction To Statistics And Data Analysis

Wentworth Medical Center As part of a long-term study of individuals 65 years of age or older, sociologists and...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Exercises 1922, a pair of dice is rolled. Find the probabilities of the given events. a. The sum is 11. b. T...

Mathematics: A Practical Odyssey

In Problems 41 and 42 solve the given problem first using the form of the general solution given in (10). Solve...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

As shown in Example 5.6.8, if a bank pays interest at a rate if I compounded m times a year, then the amount of...

Discrete Mathematics With Applications

Several years ago, management at Tuglar Corporation established a grievance committee composed of employees who...

Essentials Of Statistics For Business & Economics

Exam Scores The table shows the mathematics entrance test scores x and the final examination scores y in an alg...

College Algebra

Reminder Round all answers to two decimal places unless otherwise indicated. Unit Conversion with Exponential G...

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

Error Rates in Tax Preparation. A tax preparation firm is interested in comparing the quality of work at two of...

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