due Monday, November 3
After Mondays lecture, read carefully Lecture 15 notes and 4.1.
After Wednesdays and Fridays lectures, read carefully Lecture 16 and Lecture 17 notes as well
Solutions to review problems
1. Ten players participate at a chess tournament. Eleven games have already been played.
Prove that there is a player who has played at least 3 games.
Solution: This situation can be described by a graph
114nm 461 Second Midterm November 10, 2014 1
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o No books allowed. You may use one 8:- x 11 sheet of notes.
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Solutions for Homework #5
November 3, 2014
1. Determine the number of solutions of the equation x1 + x2 + + x10 = 100 in positive integers not
Let A be the set of all solutions of x1 + x2 + + x10 = 100 in positive integ
Solutions for Homework #4
October 28, 2014
1. How many solutions does the equation X1 X2 X3 X4 X5 = 220 have if all Xi s are positive integers?
Solution: For the product of positive integers to be a power of two, each of these integers must be
Solutions for Homework #6
November 19, 2014
1. Let T be a tree on n vertices such that the degree of each vertex is either 1 or 3.
(a) Show that n is even.
Solution: Since the number of odd-degree vertices in any graph (in particular, in a
due Friday, November 21
After Wednesdays lecture, read Lecture 22 notes.
After Fridays lecture, read Lecture 23 notes and 5.1.
After Mondays lecture, read Lecture 24 notes and 5.3
After Wednesdays lecture, re
Second Midterm Solutions
November 19, 2012
1. Please dont forget to justify your answers!
(a) Does there exist a graph whose degree sequence equals (4, 4, 3, 2, 2)?
Inspecting this sequence, we see that such a graph would have one odd-degree ve