HOMEWORK 3
SOLUTIONS
(1) Show that for each n N the complete graph Kn is a contraction of Kn,n . Solution: We describe the process for several small values of n. In this way, we can discern the inductive step. Clearly, K1 , which is just one vertex, is a
HOMEWORK 4
8 PROBLEMS DUE: WEDNESDAY, MARCH 2, 2011
(1) Draw the tree whose Prfer code is (1, 1, 1, 1, 6, 5). u (2) Determine which trees have Prfer codes that have distinct values in all positions. u (3) Let G be a connected graph which is not a tree and
Math 137
Exam 3 Review Problems
Fall 2008
Note: This is NOT a practice exam. It is a collection of problems to help you review some of the
material for the exam and to practice some kinds of problems. This collection is not necessarily
exhaustive; you sho
Math 137
Quiz 18,19- Student Strategies
Spring 2008
The following examples show work done by fourth graders. They were solving this problem:
451 287
Group I
B
A
451 100 351
451 200 251
351 100 251
251 80 171
251 50 201
171 7 164
201 30 171
171 7 164
C
45
Questions and Concerns
Promotion and Marketing:
Who and what role will your management play in the marketing and promotion
of the record, if it be any?
For promotion, my management will be going through Rocafella Records to
promote.
What platforms will
MATH 137A Midterm
Friday, February 11, 2011
Solutions
1. Determine whether K4 contains the following (give an example or a proof of nonexistence). (a) A walk that is not a trail. (b) A trail that is not closed and is not a path. (c) A closed trail that is
HOMEWORK 3
8 PROBLEMS DUE: WEDNESDAY, FEBRUARY 16, 2011
(1) Show that for each n N the complete graph Kn is a contraction of Kn,n . (2) For n N, can Kn be a contraction of Km,n if m < n? (3) The complete tripartite graph Kr,s,t consists of three disjoint
HOMEWORK 2
SOLUTIONS
(1) Let G be a simple graph where the vertices correspond to each of the squares of an 8 8 chess board and where two squares are adjacent if, and only if, a knight can go from one square to the other in one move. What is/are the possi
HOMEWORK 2
8 PROBLEMS DUE: WEDNESDAY, FEBRUARY 2, 2011
(1) Let G be a simple graph where the vertices correspond to each of the squares of an 8 8 chess board and where two squares are adjacent if, and only if, a knight can go from one square to the other
HOMEWORK 1
SOLUTIONS
(1) Let A = cfw_3, 4, 5, B = cfw_3, 4, C = cfw_4. Find D = A B C . Solution: Recall from class that A B = (A \ B ) (B \ A). That is, A B contains all elements that lie in A but not in B and all elements that lie in B but not in A. Not
HOMEWORK 1
8 PROBLEMS DUE: WEDNESDAY, JANUARY 19, 2011
(1) Let A = cfw_3, 4, 5, B = cfw_3, 4, C = cfw_4. Find D = A B C . (2) Suppose 70% of Californians like cheese, 80% like apples and 10% like neither. What percentage of Californians like both cheese a
MATH 012-_ Prealgebra Part 2
Instructor Name:_
Term_
Office hours: _
Phone: 732 224 _
email: _
TENTATIVE CLASS SCHEDULE changes will be made as appropriate
CLASS
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
DATE
SECTIONS
COVERED
Review: Whole
Numbers and In