General Info  Daytoday
Learning TeX: You'll need to install an editor (my favorite for Macs is TeXShop, and I've heard TeXMaker is good for other platforms). You'll also need a TeX distribution; everything is linked to from the math department's page on TeX. A good overall guide to learning LaTeX is the Not So Short Guide. I use TikZ for pictures; the manual I use for this is Till Tantau's PGF Manual, but really I learned by digging around the TikZ example database (in general, TeXample.net is awesome). I also have a samle TeX file on my teaching page.
Week 1  1.1, 1.2: Definitions, examples of problems in graph theory, isomorphisms. Paths, walks, cycles, components, bipartite graphs, Eulerian graphs.  
Due 3/30: 1.1 #10, 11, 14, 15, 25, 29.  
Week 2 
1.3, 1.4: Vertex degrees, extremal problems, degree sequences. Directed graphs, de Bruijn cycles, orientations. Slides: Hypercube for k=4, Degree sequences 

Due 4/6: 1.1 #30, 1.2 #1, 4, 12, 15, 18, 38, 42, 1.3 #9, 22 ((c) is extra credit)  
Quiz Tuesday 4/10: Chapter 1. (Solutions)  
Week 3  2.1: Trees and distance, spanning trees, radius and diameter.  
Due 4/13: 1.3 #8, 18, 25, 32, 44, 63, 1.4# 8, 10, 14, 2.1 #2, 18 Template: .tex 

Week 4 
2.2: Enumeration of trees, Cayley's formula, Prufer code. Counting spanning trees, deletioncontraction, the matrix tree theorem, graceful labelings. Pictures from class 

Due 4/20: 2.1 # 13, 40, 44, 47, 62, 68, 2.2 # 1, 8 Template: .tex 

Quiz Tuesday 4/24: Sections 2.1, 2.2. (Solutions)  
Week 5 
2.3: Minimum spanning trees (Kruskal's algorithm), shortest paths (Dijkstra's algorithm). Slides A survey article on applications for labeled graphs, and more modern A Dynamic Survey of Graph Labeling 

Due 4/27: 2.2 #3, 10, 23, 31, 33, 2.3 #2, 4, 10 Template: .tex 

Week 6  3.1: Matchings, Hall's theorem, minmax theorems, maximum matchings, independent sets, vertex and edge coverings. Matchings review slide [P Hall 1935] [Mirsky 1971] [M Hall 1948] [Rizzi 2000]  
Midterm: Chapters 1 and 2. Out Monday, in Friday. (Solutions)  
Recommended problems for 5/4: 2.3 #6, 20, 23, 24, 3.1 #2, 3, 8, 11  
Week 7  4.1, 4.2: Cuts, connectivity, edgeconnectivity, blocks, kconnected graphs, Menger's theorem, line graphs.  
Due 5/11: 3.1 #1, 3, 9, 12, 18, 30, 42 Template: .tex  
Week 8  4.3: Network flow problems, maxflow mincut theorem, FordFulkerson algorithm.  
Quiz Tuesday 5/15: Sections 3.1, 4.1, 4.2. (Solutions)  
Due 5/18: 4.1 #1, 7, 10, 14, 20, 25; 4.2 #8, 2, 22.  
Reading for Friday 5/18: 4.2 pp166170 (stop before Thm 24), 4.3 pp176178. (We'll talk about augmenting paths)  
Week 9  5.1, 6: Vertex colorings, bounds on chromatic numbers. Planar graphs, Euler's formula,.  
Reading for Monday 5/21: 4.3 pp179184 (stop before supplies and demands), 5.1 pp 191193. Reading for Tuesday and Wednesday: Finish 5.1. Reading for Friday: 6.1.
 
Due 5/25: 4.2 #23, 4.3 #2, 5, 13, 5.1 # 1, 19, 31, 38 I suggest that you get through as many of the () problems as you have time for.  
Week 10  6: Kuratowski's theorem, five and four color theorems.  
Suggested problems: 6.1 # 3, 5, 11, 25, 30.  
Final exam: out 5/25, due 6/2 at 2pm. (put it under my door) 
Recent posts on graph theory (and other combinatorial topics):
math.CO on arXiv
Journal of Graph Theory