COS 554 SPRING 2009 HW #4  DUE TUESDAY 2/17/09
Problem 1 below,   10 points
p. 1105: C.2- 3,   10 points
p. 1106: C.2- 9,   15 points
p. 1106: C.2-10,   15 points
p. 1117: C.4- 4,   10 points
p.  98:   5.2-4,   15 points
p.  99:   5.2-5,   15 points
p. 117:   5.4-1,   10 points
********** Problem Notes *********,
The word "show" means the same thing as "prove." In general, I expect you 
to include a reason for every answer.

Any time that the problems ask you to write pseudo-code, I want you to 
write working programs. The programs should include some representative 
data and be easy to read and should include comments. You can add comments 
to Logo programs using ";". Unless explicit language requirements are 
stated, you may use any of the four languages C, Pascal, LISP or Logo in 
this course. For many short problems, Logo will be the fastest language 
for coding.

As noted in the syllabus, I expect programs to come with printed source 
code and printed sample output. The source code should be comprehensible 
and contain comments.

PROBLEM 1: Carefully prove the following result: Let G be a graph, and a, 
b be distinct vertices in G. If there are two different simple paths 
between a and b, then there must be a simple cycle in G of length >= 3.

For all problems where it makes sense, carefully construct a probability 
space for this problem, and base your answer on this probability space. In 
particular, give reasons for choosing the sample space and the probability 
distribution.