Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 3, Problem 19E
Suppose that David is the divider and Paula is the chooser.
a. Is the cut shown in
b. Is the cut shown in
c. Is the cut shown in
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T2.3: Prove that there exists a connected graph with degrees d₁ ≥ d₂ >> dn if and only
if d1, d2,..., dn is graphic, d ≥ 1 and di≥2n2. That is, some graph having degree
sequence with these conditions is connected.
Hint - Do not attempt to directly prove this using Erdos-Gallai conditions. Instead work with a
realization and show that 2-switches can be used to make a connected graph with the same degree
sequence. Facts that can be useful: a component (i.e., connected) with n₁ vertices and at least
n₁ edges has a cycle. Note also that a 2-switch using edges from different components of a forest
will not necessarily reduce the number of components. Make sure that you justify that your proof
has a 2-switch that does decrease the number of components.
T2.2 Prove that a sequence s d₁, d₂,..., dn with n ≥ 3 of integers with 1≤d; ≤ n − 1 is the
degree sequence of a connected unicyclic graph (i.e., with exactly one cycle) of order n if and only
if at most n-3 terms of s are 1 and Σ di = 2n.
(i) Prove it by induction along the lines of the inductive proof for trees. There will be a special
case to handle when no d₂ = 1.
(ii) Prove it by making use of the caterpillar construction. You may use the fact that adding an
edge between 2 non-adjacent vertices of a tree creates a unicylic graph.
I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)
Chapter 3 Solutions
Excursions In Modern Mathematics, 9th Edition
Ch. 3 - Henry, Tom, and Fred are breaking up their...Ch. 3 - Alice, Bob, and Carlos are dividing among...Ch. 3 - Angie, Bev, Ceci, and Dina are dividing among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing among...Ch. 3 - Allen, Brady, Cody, and Diane are sharing a cake....Ch. 3 - Carlos, Sonya, Tanner, and Wen are sharing a cake....Ch. 3 - Four partners Adams, Benson, Cagle, and Duncan...Ch. 3 - Prob. 8ECh. 3 - Suppose that Angelina values strawberry cake twice...Ch. 3 - Suppose that Brad values chocolate cake thrice as...
Ch. 3 - Suppose that Brad values chocolate cake four as...Ch. 3 - Suppose that Angelina values strawberry cake five...Ch. 3 - Karla and five other friends jointly buy the...Ch. 3 - Marla and five other friends jointly buy the...Ch. 3 - Suppose that they flip a coin and Jackie ends up...Ch. 3 - Suppose they flip a coin and Karla ends up being...Ch. 3 - Suppose that they flip a coin and Martha ends up...Ch. 3 - Suppose that they flip a coin and Nick ends up...Ch. 3 - Suppose that David is the divider and Paula is the...Ch. 3 - Suppose that Paula is the divider and David is the...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing a cake...Ch. 3 - Allen, Brady, Cody; and Diane are sharing a cake...Ch. 3 - Prob. 27ECh. 3 - Four partners are dividing a plot of land among...Ch. 3 - Prob. 29ECh. 3 - Five players are dividing a cake among themselves...Ch. 3 - Four partners Egan, Fine, Gong, and Hart jointly...Ch. 3 - Four players Abe, Betty, Cory, and Dana are...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Ana, Belle, and Chloe are dividing four pieces of...Ch. 3 - Andre, Bea, and Chad are dividing an estate...Ch. 3 - Five heirs A,B,C,D, and E are dividing an estate...Ch. 3 - Oscar, Bert, and Ernie are using the method of...Ch. 3 - Anne, Bette, and Chia jointly own a flower shop....Ch. 3 - Al, Ben and Cal jointly own a fruit stand. They...Ch. 3 - Ali, Briana, and Caren are roommates planning to...Ch. 3 - Anne, Bess and Cindy are the roommates planning to...Ch. 3 - Prob. 51ECh. 3 - Three players (A,B and C) are dividing the array...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Five players (A,B,C,D,andE) are dividing the array...Ch. 3 - Four players (A,B,C,andD) are dividing the array...Ch. 3 - Prob. 57ECh. 3 - Queenie, Roxy, and Sophie are dividing a set of 15...Ch. 3 - Ana, Belle, and Chloe are dividing 3 Choko bars, 3...Ch. 3 - Prob. 60ECh. 3 - Prob. 61ECh. 3 - Prob. 62ECh. 3 - Prob. 63ECh. 3 - Prob. 64ECh. 3 - Three players A, B, and C are sharing the...Ch. 3 - Angeline and Brad are planning to divide the...Ch. 3 - Prob. 67ECh. 3 - Efficient and envy-free fair divisions. A fair...Ch. 3 - Suppose that N players bid on M items using the...Ch. 3 - Asymmetric method of sealed bids. Suppose that an...Ch. 3 - Prob. 73E
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- = == T2.1: Prove that the necessary conditions for a degree sequence of a tree are sufficient by showing that if di 2n-2 there is a caterpillar with these degrees. Start the construction as follows: if d1, d2,...,d2 and d++1 = d = 1 construct a path v1, v2, ..., vt and add d; - 2 pendent edges to v, for j = 2,3,..., t₁, d₁ - 1 to v₁ and d₁ - 1 to v₁. Show that this construction results vj in a caterpillar with degrees d1, d2, ..., dnarrow_forwardDo the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
- 12. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.508.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x + 16 dx X Need Help? Read It SUBMIT ANSWER 13. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.512.XP. ASK YOUR TEA Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx 8)(2x + 1) Need Help? Read It SUBMIT ANSWER 14. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.518.XP. Find the area of the region under the given curve from 1 to 5. y = x² +7 6x - x² Need Help? Read It ASK YOUR TEAarrow_forwardLakshmi planted 20 begonias, but her neighbor’s dog ate 7 of them. What percent of the begonias did the dog eat?arrow_forwardDETAILS MY NOTES SESSCALCET2 6.3.012. 6. [-/1 Points] Evaluate the integral. x-4 dx x² - 5x + 6 Need Help? Read It SUBMIT ANSWER 7. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.019. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x²+1 (x-6)(x-5)² dx Need Help? Read It SUBMIT ANSWER 8. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.3.021. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ✓ x² 4 +4 dxarrow_forward
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