MATH 1050, Homework 5
Kiumars Kaveh
September 27, 2013
Due date: Wednesday October 2, 2013
Problem 1:(a) Let G = (V, E ) be a graph. For a vertex v V let d(v )
denote the degree of v , i.e. the number
Chapter 2. Strings, Sets, and Binomial Coefcients
In fact, I tried it out with two integers, each having more than one thousand digits. It
found the product in about one second. Ever the skeptic, Zori
MATH 1050, Homework 2 Solutions
Kiumars Kaveh
September 4, 2013
Problem 1: Let n and k be positive integers. Give a formula for the number of solutions of n = x1 + + xk where the xi are positive integ
MATH 1050, Homework 6
Kiumars Kaveh
October 3, 2013
Due date: Wednesday October 9, 2013
Problem 1: Let v , w be two vertices of a graph G. Show that if there is
a walk between v and w then there is a
MATH 1050, Homework 4
Kiumars Kaveh
September 18, 2013
Due date: Wednesday September 25, 2013
Problem 1: Suppose you have a set A with 10 (distinguishable) elements
e.g. A = cfw_1, . . . , 10. In how
MATH 1050, Homework 3
Kiumars Kaveh
October 12, 2013
Due date: Wednesday September 18, 2013
Problem 1: The binomial expansion theorem states that (a+b)n = n
i=0
(a) Extend this theorem to sum of three
MATH 1050, Homework 7
Kiumars Kaveh
October 18, 2013
Due date: Wednesday October 23, 2013
s
Problem 1: Prove by induction that R(r, s) r+2 . Hint: recall the
r1
inductive proof of Ramseys theorem stat
MATH 1050, Homework 8
Kiumars Kaveh
October 25, 2013
Due date: Friday November 1st, 2013
Problem 1: In the weighted graph below, apply Kruskals algorithm to
nd a minimal spanning tree. In each step of
Department of Mathematics
University of Pittsburgh
MATH 1050 (Combinatorics)
Midterm, Fall 2013
Instructor: Kiumars Kaveh
Last Name:
Student Number:
First Name:
TIME ALLOWED: 50 MINUTES. TOTAL: 50+2
N
MATH 1050, Homework 10
Kiumars Kaveh
November 28, 2013
Due date: Wednesday December 4, 2013
Problem 1: In the graph below use Phillip Halls theorem to prove that
there is no perfect matching.
Problem
MATH 1050, Homework 9
Kiumars Kaveh
November 1, 2013
Due date: Friday November 8th, 2013
Problem 1: (a) Write down the linear programming problem corresponding to the max ow problem in the network bel