Spring 2007
Instructor: Sergi Elizalde
Lectures: MWF 12:301:35 in Kemeny 105
Xperiod: Tu 1:001:50
Office Hours: M 1:353:30, F 11:3012:30
Office: Kemeny 332
Email:
Phone: 6468191
Announcements
Here is this week's homework assignment.
The final will be a takehome exam, handed out on
Friday, May 25 and due on Wednesday, May 30.
You are responsible for everything covered in the course (including Friday's
class).
Course description
This course will cover the fundamental concepts of Graph Theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, matchings, networks, paths and cycles, graph colorings, and planar graphs. Famous problems in Graph Theory include: Minimum Connector Problem (building roads at minimum cost), the Marriage Problem (matching men and women into compatible pairs), the Assignment Problem (filling n jobs in the best way), the Network Flow Problem (maximizing flow in a network), the Committee Scheduling Problem (using the fewest time slots), the Four Color Problem (coloring maps with four colors so that adjacent regions have different colors), and the Traveling Salesman Problem (visiting n cities with minimum cost).
Textbook
Introduction to Graph Theory by Douglas B. West, Second edition (available at Wheelock Books).
Tentative syllabus
This syllabus is subject to change, but it should give you an idea of the topics I am planning to cover.
Chapters 
Brief Description 

Week 1  1.1, 1.2 
Basic definitions, isomorphisms, walks,
cycles and bipartite graphs 

Week 2  1.3, 1.4  Components, cutedges, Eulerian graphs, vertex degrees and degree sequences, directed graphs  
Week 3  2.1, 2.2 
Eulerian digraphs, trees and
distance 

Week 4  2.2, 2.3  Counting spanning trees and the matrix tree theorem, minimal spanning trees and shortest paths  
Week 5  3.1, 3.3 
Matchings, Hall's theorem and coverings, maximum
matchings, factors 

Week 6  4.1, 4.2 
Cuts and connectivity 

Week 7 
4.2, 4.3 
Network
flow problems, maxflow mincut theorem 

Week 8  5.1, 5.2 
Vertex colorings, bounds on chromatic
numbers and Mycielski's construction 

Week 9  5.3, 6.1 
Chromatic polynomials, chordal graphs,
planar graphs 

Week 10  6.2, 6.3 
Euler's formula and Kuratowski's theorem,
five and four color theorems 
Grading
The course grade will be based on the homework (20%), two midterms (25% each), a final exam (25%), and class participation (5%).
Homework
There will be homework due roughly every week. It will consist typically of a reading assignment (of the part of the book covered in class) and some problems. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.
Exams
On the midterms and the final exam you must work on the problems on
your own. No collaboration permitted in the exams.
Students with
disabilities: Students with learning,
physical, or psychiatric disabilities enrolled in this course that may need
disabilityrelated classroom accommodations are encouraged to make an office
appointment to see me before the end of the second week of the term. All
discussions will remain confidential, although the Student Disability
Services office may be consulted to discuss
appropriate implementation of any accommodation requested.
Last modified on May 13, 2007.