Prerequisites: 
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): 6256682 Email: reiner@math.umn.edu 

Classes:  MonWed 2:304:25pm in Burton Hall 123 
Office hours:  Thursdays and Fridays, 2:303:20pm. 
Required text:  Modern graph theory by B. Bollobas, (1998, Springer Graduate Texts in Mathematics 184). 
Course content: 
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 
Homework, exams, grading: 
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 takehome midterms and final exam are openbook, openlibrary, openweb, 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 wellexplained 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 n1", not n2) 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. 
Topic  Author  Title/info 

List of open problems and conjectures in graph theory 
Doug West's Bonato and Nowakowski's IRMACS 
problems page
Sketchy Tweets: 10 minute conjectures in graph theory Open Problem Garden for Graph Theory 
Probabilistic method  N. Alon and J. Spencer  The probabilistic method
WileyInterscience, 2000 
Surfaces and graphs on them  W.S. Massey  (Chap. 1 of) Algebraic topology: an introduction SpringerVerlag Graduate Texts in Math 56 
P. Giblin  Graphs, surfaces and homology
Cambridge Univ. Press 2010 