Math 2243 and either Math 2283 or 3283 (or their equivalent).
Students will be expected to know calculus and linear algebra
(e.g. familiarity with determinants and eigenvalues is expected),
and be ready to read, understand and write proofs.
|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
|Classes:||Mon-Wed 2:30-4:25pm in Burton Hall 123|
|Office hours:||Thursdays and Fridays, 2:30-3:20pm.|
|Required text:||Modern graph theory by B. Bollobas, (1998, Springer Graduate Texts in Mathematics 184).|
Graphs are networks of vertices (nodes) connected by edges.|
They are interesting objects in mathematics, but also usefully model
problems in computer science, optimization, and social science.
This is a first course in graph theory, emphasizing classical topics, such as
|Title||Author(s), Publ. info||Location|
| Introduction to graph theory||D. West, Prentice Hall 1996||On reserve in math library|
|Graph theory||R. Diestel||The author's download page|
|Schaum's outlines: graph theory||V. K. Balakrishnan||On reserve in math library|
|A course in combinatorial optimization||A. Schrijver||The author's download page|
There will be 5 homework assignments due usually every other week, but
I encourage collaboration on the homework, as long as each person understands the solutions,
writes them up in their own words, and indicates on the homework page their collaborators.
The take-home midterms and final exam are open-book, open-library, open-web,
but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed.
Late homework will not be accepted. Early homework is fine, and can be left in my mailbox
in the School of Math mailroom near Vincent Hall 105.
Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer.
Complaints about the grading should be brought to me.
|Grading scheme :||
|Assignment or Exam||Due date||Problems from Bollobas text|
|Homework 1||Wed, Feb. 6||
Chap. I # 1,2,3,7,17,18,19,24,26,35
(Correction in #17, 18, and hint for #19:
In #17, add the assumption that n is at least 2 throughout the problem.
In #18, change "with k components" to "with k components, none of which are isolated vertices".
In #19, as a hint, I might suggest that you characterize the degree sequences of forests that have
a fixed number k of components that are not isolated vertices
along with a fixed number p of isolated vertex components.)
Chap. III # 40, 41
|Homework 2||Wed, Feb. 20||
Chap. I # 38,85,94
(Typo corrections in #94:
the calligraphic "F" should be a calligraphic "T",
and it should say "diameter at most n-1", not n-2)
Chap. III # 12,18,19,28,82
|Exam 1||Wed, Feb. 27||Here is Midterm 1 in PDF.|
|Homework 3||Wed, Mar. 27||
Chap. III # 1, 44, 45, 46, 54, 56
plus these Exercises on orientations in PDF.
|Homework 4||Wed, Apr. 10||
Chap III # 14
Chap. V # 1,3,5,23,24, 45,46,47,49
(add the hypothesis that G is bridgeless to #23)
|Exam 2||Wed, Apr. 17||Here is Midterm 2 in PDF.|
|Homework 5||Wed, May 1||
Chap. VI # 1,2
Chap. VII # 1,2,3,4,6
Chap. X # 1,2,10
|Final Exam||Wed, May 8||Here is the Final exam in PDF.|
List of open problems and
conjectures in graph theory
Bonato and Nowakowski's
Sketchy Tweets: 10 minute conjectures in graph theory
Open Problem Garden for Graph Theory
|Probabilistic method||N. Alon and J. Spencer|| The probabilistic method
|Surfaces and graphs on them||W.S. Massey|| (Chap. 1 of) Algebraic topology: an introduction
Springer-Verlag Graduate Texts in Math 56
|P. Giblin|| Graphs, surfaces and homology
Cambridge Univ. Press 2010