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Course Syllabus 575/513 Chapter references are to Tucker textbook:Applied Combinatorics, Alan Tucker, 6th edition, Wiley, 2012. Additional materials from Pearls in...
Homework Seven Quick Answers 1. 2 (263 103) 5.1.18 2. You can choose 21 21 integer pairs. In the given range 11 are even, 10 are odd. So: (11 11 10 10)/21 21...
Computer Science 575 / Math 513 Fall 2014 December 10 Office hours this week for 575/513: Wednesday 1 2:30 (no office hours monday or tuesday, except by appointment...
575/513 Homework Assignments HwkOne HwkTwo Hwk2Ans HwkThree Hwk3Ans HwkFour Hwk4Ans HwkFive Hwk5Ans HwkSix Hwk6Ans HwkSeven Hwk7Ans HwkEight Hwk8Ans HwkNine Hwk9Ans...
Homework Six quick answers 1. 27 cells, 14 black, 13 blue. Center cell is blue. HAM path must be 27 long, must start and end with black (the 14 count color). But...
Homework Nine Quick Answers 1. C(12,6) 2. Generator is (1 x x2)50 seek coefficient of x40 This begins C(89,40) C(50,1) C(86,37) C(50,2) C(83,34)... 3. Just pick...
Homework Assignment Nine You may collaborate on numbers 4,5, 8. Notation in brackets are references to problems in Tucker, 5th edition. 1 Find the coefficient of...
Homework Assignment 10 Quick Answers 1. an 2an 1 an 2 2. an 2an 1 (2n 3 an 3) 3. an an 2 2 an 3 4 an 4 4. 3n 1/2(n2 3n) or (1 Sum1,n ((k...
Homework 11 Quick Answers 1. 69 C(6,1) 59 C(6,2) 49 C(6,3) 39 ... 2. C(52,8) C(13,1) C(48,4) C(13,2) 3.SIGMA k 0,n ( 1)k C(n,k) 2k (2n 1 k)! 4. 1...
Homework 12 Quick Answers 1. For example,pi2 is (a b c d) 2. pi2 and pi3 3. 1/4 2 64 2 2 16 2 32 4. n even: 1/2(3 2n 1); n odd 1/2(3 2n 1 3 2(n 1)/2))...
Homework Assignment Twelve You may collaborate on 9 1 9.1.4 textbook editions 3,4,5,6 1 9.1.12 textbook editions 3,4,5,6 1 9.2.4 textbook editions...
Homework Assignment Ten You may collaborate on numbers 1,3,5,7. 1 Find a recurrence for the number of n letter sequences using letters A, B, and C, such that any...
Homework Assignment 11 You may collaborate on problem numbers 3,5,6 1 How many ways are there to roll 9 distinct dice so that all 6 faces appear? 8.2.2 1 What...
Homework Assignment Eight You may collaborate on 3, 6, 12. Citations in indicate problem numbers in Tucker, 6th edition. 1 Show the correctness of this binomial...
Homework Assignment Seven 1 How many different license plates involving 3 letters and 3 digits are there if the three letters appear at the beginning or at the...
Homework Assignment Six 1. Consider 27 cubes arranged in a 3x3x3 array. Form an associated graph with each cube viewed as a vertex, and with two vertices adjacent...
Quick Answers Homework Assignment 5 1. Suppose a connected graph G has 20 edges. What is the maximum number of vertices possible in G? Answer: 21 this is the tree...
CS 575 / Math 513Homework Three Quick Answers 1. Choose a max length path in G with endpoints a, b. Take a. Its links must go back into path, else path could...
Homework Five CS 575 / Math 513 You may collaborate on #2 and #6. 1. Suppose a connected graph G has 20 edges. What is the maximum number of vertices possible in...
Computer Science 575 / Math 513 Homework Assignment Four Collaboration permitted on: 6, 8,9,10 Due: Tuesday, September 30, in class RobbieMoll 17 Feb 2009
Computer Science 575 Math 513 Fall 2014 Homework 3 You may collaborate on #2,8,9 1. Suppose d 1, and for graph G every vertex has degree d. Show that G must...
Course Administration CS 575 / Math 513 Instructor: Robert Moll CS Bldg room 276; moll #64;cs.umass.edu; 545 4315; Office hours TU 3 4; WED 1 2:30; TH...
Computer Science 575 Homework Assignment #2 Assignment is attached at the bottom of this page (pdf format). You may collaborate on problems 3 and 7. Due date: Tuesday...
Computer Science 575 Fall 2014 Homework Assignment 1 All problems are from the textbook, fifth edition. I`ve also attached an image of the problems if you are using...
Course Resources CS 575 / Math 513 Textbook: Alan Tucker, Applied Combinatorics (Wiley) 6th edition. On sale at textbook annex Other useful texts: Roberts...
575/513 Final Fall 2006 Answers 1. How many distinct four digit numbers have the property that their digits sum to 31? Answer: Via generating functions look for...
Homework 8 Quick Answers 1. Rewrite the generic term as C(m,m k) C(n,r k). In this form the target, C(m r,m n) accounts for all paths to location m r at depth m n...
RobbieMoll 2012 03 13
CS 575 / Math 513 Homework 4 Quick Answers 1. a) Kn for odd n; b) K2; c) r,s both even. 2. No this would be an Euler cycle on the graph of board cells, with...
CS 575/ Math 513 Homework 2 Answers Homework Two Answers 1. vertices are labeled 0 16. Each vertex has arcs to next 3 (e.g. 8 9, 10, 11). Second player...
Course Grading 575/513 Grading: 50% homework problems; 15% midterm; 35% final. Also: you must pass the final to get a C in the class. Collaborative solutions...
CourseSyllabus HomeworkAssignments CourseAdministration CourseGrading CourseResources Home
Top Menu of Moll575 Web This topic defines the menu structure of the Moll575 web, used by the TopMenuSkin. 1 Web` Create New Topic...
A Sample Midterm Computer Science 575 / Mathematics 513 Combinatorics and Graph Theory Midterm Exam October 19, 2006 (closed book, 75 minutes, in class) 1. (16) Suppose...
Elementary Java Resource Web LoopingLink RobbieMoll 17 May 2007
Statistics for Moll575 Web Month: Topic views: Topic saves: File uploads: Most popular topic views: Top contributors for topic save and...
Homework Assignment Eleven Quick Answers 1. 8.2.2 6 10 C(6,2)5 10 C(6,3)4 10 .. 2. 8.2.4 prime factors: 2,3,5,7, so: 420 ...
Course Homework Assignments HomeworkOne HomeworkTwo HwkTwoanswers HomeworkThree HwkThreeanswers HomeworkFour HwkFouranswers HomeworkFive...
Homework Ten Quick Answers 1. 7.1.8 Use identity C(n,k) C(n 1,k) C(n 1,k 1) 2. 7.1.18 a. An 2An 1 An 2; b. An An 2 2An 1 4An 4 3. 7.1.22 An 2An 1 2 (n 1) 4. 7....
Homework Assignment Twelve Quick Answers 1. 9.1.4 2. 9.1.12 pi2 and pi7 don...
Homework Assignment Nine Quick Solutions 1. 6.2.4 C(14,9) C(9,4) 2. 6.2.18 a.C(r 1,r 8); b. C(r/2 7,r/2) 3. 6.2.24 C(89,40) C(86,37)C(50,1) C(83,34)C(50,2).....
Computer Science 575/ Mathematics 513 Combinatorics and Graph Theory Final Exam May 14, 2005 Show all you work! 1. Given two copies each of the letters a,b,c,d,e...
Homework Assignment Twelve Due: in class on Tuesday, December 12 last day of class (all work due at that time!) 1. 9.1.2 2. 9.1.12 3. 9.2.4 4. 9.2.10 5. 9.3.4...
Homework Eight Quick Answers 1. 5.4.10 C(32,4); C(27,4); C(17,4) 2. 5.4.22 C(17,2) C(14,2) C(11,2) C(8,2) C(5,2) 1 3. 5.4.48 solved at end of chapter 4....
Homework Seven Quick Answers 1. 5.1.6 n (n 1) 2. 5.1.10 23, that is (1 3) (1 5) ...
Homework Assignment Eleven Due: in class, Thursday, November 30 (note Thursday collection day) 1. 8.2.2 2. 8.2.4 3. 8.2.12 4. 8.2.18 5. 8.2.28 6. 8.3.2 a,d 7. 8....
Homework Assignment Ten Due in class on 11/21 1. 7.1.8 2. 7.1.18 3. 7.1.22 4. 7.1.26 5. 7.1.34 6. 7.3.2 7. 7.4.2 RobbieMoll 14 Nov 2006
Homework Assignment Nine Due in class on Tuesday, November 14 1. 6.2.4 2. 6.2.18 3. 6.2.24 4. 6.2.30 5. 6.3.14 6. 6.3.22 7. 6.4.10 8. 6.5.2e 9. 7.1.2 RobbieMoll...
Homework Eight Due: Tuesday, November 7, in class 1. 5.4.10 2. 5.4.22 3. 5.4.48 4. 5.4.54 5. 5.5.14,d,f 6. 5.5.22 7. 5.5.26 8. 5.5.34 9. 6.1.2 10. 6.1.6 11. 6.1....
Homework Assignment Seven Due date: October 31, in class 1. 5.1.6 2. 5.1.10 3. 5.1.12 4. 5.1.18 5. 5.1.20 6. 5.1.24 7. 5.1.30 8. 5.1.34 9. 5.1.42 10. 5.2.2 11. 5....
Lecture Eleven: Matching The fundamental theorem about unweighted bipartite matching is Hall` theorem: a bipartite graph (X,Y,E) has a complete match(i.e. a match...
Lecture Summaries LectureFive LectureSix LectureSeven LectureEight LectureNine LectureTen LectureEleven RobbieMoll 26 Sep...
Telegraphic Answers to Homework Assignment Five 1. 3.1.2 21 2. 3.1.18 use the fact that if c1 and c2 are centers, and b1 and b2 are leaves that witness for the...
Homework four quick answers Brief Answers 1. 2.1 2 (a) any odd n; (b) K2 (c) both r,s even 2. 2.1 4 lift twice 6 odd degree vertices. connect 2 of them, then...
Lecture Seven RobbieMoll 16 Oct 2006
Lecture Ten: Network Flows Lecture today follows the text fairly closely A network is a loop free directed connected graph with a unique source (a), sink...
Homework Assignment Six 1. 4.4.2 2. 4.4.8 3. 4.2.13 4. 4.2.6 5. 4.3.2 a,b 6. Two spanning trees on a Graph N, say T1 and T2, are `neighbors` if T2 can be obtained...
Computer Science 575 / Mathematics 513 Combinatorics and Graph Theory Midterm Exam March 10, 2005 1. (15) Characterize trees that have Euler trails. 2. (15) An...
Lecture Nine: Trees, part 2 Recall a tree is connected graph without circuits If G is a connected, undirected graph, then it has a spanning tree T a...
Homework Five 1. 3.1 2 2. 3.1 18 3. 3.1 24 4. 3.1 26 5. 3.1 28 6. 3.1 30 7. 3.2 6 8. 3.2 16 a Due Tuesday, October 10, in class RobbieMoll...
Lecture Eight: Trees, part 1 Def a tree is connected graph without circuits Textbook quickly switched to rooted trees: trees with distinguished `root`...
Homework Three Quick Answers 1. 1 supp 4 (p. 49) 11 vertices is minimum. K11 has 55 edges, K10 has 45 2. 1 supp 10 Consider (a) shortest path from a to b, where a...
Homework Assignment Four 1. 2.1 2 2. 2.1 4 3. 2.1 10 4. 2.1 16 5. 2.2 4 (d,e) 6. 2.2 16 7. 2.2 20 8....
Homework Two Answers 1. 1.1.4 ...
Lecture Six Notes Lecture six covers the basics of Euler cycles and Hamiltonian circuits and their variants. The fundamental theorem about Euler cycles, due to Euler...
Lecture Five: Wagner`s Theorem Every planar graph has a planar drawing constructed using just straight lines. Def a max planar graph (mpg) is a planar graph...
Homework Assignment Three All problems from the text, except 5. 1. 1 supp 4 (p. 49) 2. 1 supp 10 3. 1.3 4 4. 1.3 12 5. Given this degree sequence: (4,4,4,4,3,...
Homework Assignment Two All numbered homeworks are from the Tucker text 1. 1.1.4 2. 1.1.20 3. Prove that no graph with two or more vertices has the...
Homework Assignment One All problems are from the textbook 1 problem 8, page 401 2 problem 11, page 401 3 problem 14, page 401 4 problem 22, page...
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Homework Assignment Twelve Due: in class on Thursday, May 12 last day of class (all work due at that time!) 1. 9.1.2 2. 9.1.12 3. 9.2.4 4. 9.2.10 5. 9.3.4 6. 9....
Course Assignments CS 575 / Math 513 AssignmentOne AssignmentTwo AssignmentThree AssignmentFour AssignmentFive AssignmentSix AssignmentSeven AssignmentEight AssignmentNine...
Homework Assignment Eleven Due: in class, Tuesday, 5/3 1. 8.2.2 2. 8.2.4 3. 8.2.12 4. 8.2.18 5. 8.2.28 6. 8.3.2 a,d 7. 8.3.4 8. 8.3.12 RobbieMoll 20 Apr 2004
Homework Assignment Ten Due in class on 4/19 1. 7.1.8 2. 7.1.18 3. 7.1.22 4. 7.1.26 5. 7.1.34 6. 7.3.2 7. 7.4.2 8. 7.5.8 RobbieMoll 13 Apr 2004
Homework Assignment Nine Due in class on Tuesday, April 12 1. 6.2.4 2. 6.2.18 3. 6.2.24 4. 6.2.30 5. 6.3.14 6. 6.3.22 7. 6.4.10 8. 6.5.2e 9. 7.1.2 RobbieMoll...
Homework Assignment Eight Due: Tuesday, April 5, in class 1. 5.4.10 2. 5.4.22 3. 5.4.48 4. 5.4.54 5. 5.5.14,d,f 6. 5.5.22 7. 5.5.26 8. 5.5.34 9. 6.1.2 10. 6.1.6...
/Moll575 The 1 web of TWiki. TWiki is a Web Based Collaboration Platform for the Enterprise.
Homework Assignment Seven Due date: March 29, in class 1. 5.1.6 2. 5.1.10 3. 5.1.12 4. 5.1.18 5. 5.1.20 6. 5.1.24 7. 5.1.30 8. 5.1.34 9. 5.1.42 10. 5.2.2 11. 5.2....
Homework Assignment Six 1. 3.3.6 2. 3.3.10 b 3. 4.2.13 4. 4.2.6 5. 4.3.2 a,b 6. Two spanning trees on a network N, say T1 and T2, are `neighbors` if T2 can be obtained...
Assignment Five 1. 3.1 2 2. 3.1 18 3. 3.1 24 4. 3.1 26 5. 3.1 28 6. 3.1 30 7. 3.2 6 8. 3.2 16 a now due thursday, 3/3 RobbieMoll 29 Feb 2004...
Homework Assignment Four 1. 2.1 2 2. 2.1 4 3. 2.1 10 4. 2.1 16 5. 2.2 4 (d,e) 6. 2.2 16 (or #1 on page 92) 7. 2.2 20 8. 2.3 6 9. 2.3...
Homework Assignment Three 1. 1 supp 4 (p. 49) 2. 1 supp 10 3. 1.3 4 4. 1.3 12 5. Given this degree sequence: (4,4,4,4,3,3), find two graphs with this degree...
Homework Twelve Answers RobbieMoll 14 May 2004
Homework Eleven Answers RobbieMoll 09 May 2004
Assignment Ten Solutions RobbieMoll 04 May 2004
Assignment Nine Solutions RobbieMoll 04 May 2004
Assignment Eigth Solutions RobbieMoll 04 May 2004
Assignment Seven Answers RobbieMoll 14 Apr 2004
Assignment Five Answers RobbieMoll 10 Mar 2004
Assignment Four Answers RobbieMoll 10 Mar 2004
Assignment Three Short Answers RobbieMoll 10 Mar 2004
Answers to homework assignment #2 RobbieMoll 23 Feb 2004
Answers to homework assignment #1 RobbieMoll 19 Feb 2004
All numbered homeworks are from the Tucker text 1. 1.1.4 2. 1.1.20 3. Prove that no graph with two or more vertices has the property that all its vertices have different...
Assignment number one All problems are from the textbook 1 problem 8, page 401 2 problem 11, page 401 3 problem 14, page 401 4 problem 22, page...
Computer Science 575 / Mathematics 513 Combinatorics and Graph Theory old midterm answers 1. A graph is regular if all of its vertices are of the same degree. Suppose...
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