Spring 2008
Lectures: MWF 12:301:35 in Haldeman 028
Xhour: Tu 1:001:50
Instructor: Peter Winkler
Office Hours: M 23, W 56, F 1011
Office: Kemeny 231
Email:
Phone: 6463468
Announcements
The final exam for Math 38 will be in our regular classroom, Haldeman 028. It's at 3pm Sunday June 1; you'll have 3 hours to complete the exam, but it's actually designed to take only two.
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 is the syllabus we actually covered.
Chapters 
Brief Description 

Week 1  1.1 
Definitions; bipartite graphs; chromatic number; adjacency matrix; isomorphism; decomposition;
connectedness; subgraphs and induced subgraphs 

Week 2  1.2, 1.3 
Path versus walk; cycles; cutedge and cutvertex; TONCAS for Eulerian property; sum of degrees;
extremality; induction 

Week 3  1.4 
Paths; cycles; strong digraphs; Eulerian digraphs 

Week 4  2.1, 2.2 
Equivalent definitions of tree; distance and diameter; Cayley's Theorem and Pruefer code;
recurrence for counting spanning trees; matrixtree theorem (not proof); BEST Theorem and proof; graceful tree conjecture 

Week 5  2.3 
Kruskall's algorithm and reverse version; Dijkstra's algorithm 

Week 6  3.1 
Maximal, maximum and perfect matchings; augmenting paths; Hall's marriage theorem; minmax theorems:
vertex cover versus matchings; Koenig's Theorem on edgecoloring a bipartite multigraph [not in text] 

Week 7  4.1, 4.2, 4.3 
Edgeconnectivity; blocks; kconnectedness; 2connected graphs; connectivity in digraphs;
Menger's Theorem (not proof); line graphs; feasible and maximal flows; min flow/max cut theorem (not proof) 

Week 8  5.1, 5.2 
Cartesian product; interval graphs; Brooks' Theorem; Mycielski's construction; colorcriticality;
Turan's Theorem and proof 

Week 9  6.1, 6.2 
Planar graphs versus plane graphs; nonplanarity of K5 and K3,3; faces and the dual graph; Euler's formula;
bound on number of edges; maximal planar graphs; Kuratowski's TONCAS (not proof); list coloring and Thomassen's Theorem [not in text] 

Week 10  7.2 
Necessary and sufficient conditions for Hamiltonicity; Dirac's Theorem; Gray code [not in text];
midlevels problem[not in text] 
Grading
The course grade will be based on homework and class participation (20%), two midterms (20% each), and the final exam (40%).
Midterms will be in class on Monday, April 14 and Friday, May 2: make sure you don't miss those! The final will be at the scheduled 3hour period for period 12 (MWF 12:301:35) classes, namely at 3:00 pm on Sunday June 1, and will be comprehensive.
Homework
There will be homework due most class meetings. It will consist typically of a reading assignment (of the part of the book covered in class) and one or two problems. Collaboration on the homework is permitted, provided the assignments are written up separately and independently. Names of those persons with whom you collaborated must be written on the assignment.
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 March 24, 2008.