Spring 2010
·
Instructor: Sergi Elizalde
·
Lectures: MWF 12:301:35 in
Kemeny 108
·
Xperiod: Tu
1:001:50
·
Office Hours: M 1112:30, Th 2:303:30.
·
Office:
Kemeny 332
·
Email:
· Phone: 6468191
Announcements
Here is this week's homework assignment.
The class on Friday, May 28
will be moved to the Xhour on Tuesday, May 25.
The takehome final exam
will be handed out on Wednesday, May 26, and due on June 2, the last day of
class. It will cover everything we have done up to Chapter 5 (included).
The grader for the course
is Will Chen.
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: the 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 
Definitions, examples of problems in graph theory, isomorphisms.
Paths, walks, cycles, components, bipartite graphs, Eulerian graphs. 
Week 2 
1.3, 1.4 
Vertex degrees, extremal problems, degree sequences.
Directed graphs, de Bruijn cycles, orientations. 
Week 3 
2.1 
Trees and distance, spanning trees, radius and
diameter. 
Week 4 
2.2 
Enumeration of trees, Cayley’s formula, Prüfer
code. Counting spanning trees, deletioncontraction, the matrix tree theorem,
graceful labelings. 
Week 5 
2.3 
Minimum spanning trees (Kruskal’s algorithm),
shortest paths (Dijkstra’s algorithm).

Week 6 
3.1 
Matchings, Hall's theorem, minmax theorems, maximum
matchings, independent sets,
vertex and edge coverings. 
Week 7 
4.1, 4.2 
Cuts, connectivity, edgeconnectivity, blocks,
kconnected graphs, Menger’s theorem, line graphs . 
Week 8 
4.3 
Network flow problems, maxflow
mincut theorem, FordFulkerson algorithm. 
Week 9 
5.1, 5.3 
Vertex colorings, bounds on chromatic numbers.
Chromatic polynomials. 
Week 10 
6 
Planar graphs, Euler's formula,
Kuratowski's theorem, five and four color theorems. 
Grading
The course grade will be based
on the homework (20%), two midterms (25% each), and a final exam (30%).
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. All the homework
assignments are posted here. You are
encouraged to collaborate on the homework, but what you write has to be your
own understanding of how to do the problem. You must state what sources you
have consulted, with whom you have collaborated, and from whom you have
received help. No late homework will be accepted.
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.