HW1
(Please excuse my crappy drawings in MS Paint.)
2. (a)
In this diagram, directed edges point from winners to losers. (Doing
it the other way is of course ne as long as it is clear which way youre
going.)
1
2
HW1
4. (a)
(b)
On the rst day, the rumour s
HW2
(Again, please excuse my crappy drawings in MS Paint.)
(Also, feel free to contact me (or the prof, I guess) if there are any
problems with the solutions, or if theres something unclear or whatever!)
1.2.3
(a)
There are many possible answers. Two are
HW5
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
2.3.10 and 2.4.2 were graded in detail, while the rest were checked
for completion.
2.3.
HW5
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
5.2.70 and the non-book problem were graded in detail, while the
rest were checked for c
HW3
(Again, please excuse my crappy drawings in MS Paint.)
(Also, feel free to contact me (or the prof, I guess) if there are any
problems with the solutions, or if theres something unclear or whatever!)
(It occurs to me that I have neglected to mention m
HW4
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
2.2.4d and 2.2.16 were graded in detail, while the rest were checked
for completion.
2.2
HW7
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
5.3.22 and 5.4.58 were graded in detail, while the rest were checked
for completion.
Not
Hamilton circuits (Section 2.2)
Under what circumstances can we be sure a graph has a Hamilton circut?
Theorem 1. Kn has a Hamilton circuit for n 3.
Proof. Let v1 , . . . , vn be any way of listing the vertices in order. Then v1 v2
vn v1 is a Hamilton c
HW8
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
6.2.18 and 6.3.2 were graded in detail, while the rest were checked
for completion.
Note
HW10
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
8.1.36 and 8.2.6 graded in detail, while the rest were checked for
completion.
8.1.2
He
HW9
(Feel free to contact me (pow at math.upenn.edu) (or the prof, I
guess) if there are any problems with the solutions, or if theres something unclear or whatever!)
7.1.22 and 7.5.2a were graded in detail, while the rest were checked
for completion.
Not
1
Connected Graphs
Denition 1.1. Let G = (V, E) be a graph and let x, y V . There is a path
from x to y if there is a sequence x = x1 , x2 , . . . , xn = y such that for every
i < n, (xi , xi+1 ) is an edge in E.
A path is a circuit if x = y.
a
b
For exam