Math 38: Graph Theory Spring 2004 Dartmouth College
Instructor: David Little
Office Hours: MW 3-4, TuTh 11-12
Phone: (603) 646-2960
E-mail:dlittle@dartmouth.edu

General Info/
Announcements

• 06/03/04 - Solution to Problem 7.1.26
• 06/02/04 - Homework 8 Solutions (LaTeX Source)
• 05/26/04 - Homework 7 Solutions (LaTeX Source)
• 05/19/04 - Homework 6 Solutions (LaTeX Source)
• 05/17/04 - Exam II Solutions
• 05/10/04 - Homework 5 Solutions (LaTeX Source)
• 05/05/04 - Homework 4 Solutions (LaTeX Source)
• 04/28/04 - Homework 3 Solutions (LaTeX Source)
• 04/28/04 - Exam I Solutions
• 04/19/04 - Homework 2 Solutions (LaTeX Source)
• 04/14/04 - Homework 1 Solutions (LaTeX Source)
• 04/02/04 - On Writing Proofs
• 03/29/04 - Graph Theory - Examples and Applications (LaTeX Source)
• 03/29/04 - Course Syllabus

• Graph Theory

• Graph Theory Open Problems
• Unsolved Problems - Maintained by Stephen C. Locke
• Open Problems in Graph Theory and Combinatorics - Maintained by Douglas B. West (Glossary of Terms)
• Graph Theory Tutorials
• Graph Theory - from Eric Weisstein's World of Mathematics
• Graph Theory Resources
• Graph Theory Lessons

• Homework
 Due Date Date Assigned Topics Covered Homework* -/- 03/29 Introduction: Examples and Applications of Graph Theory Read Chapter 1.1 04/09 03/31 Basic Definitions and Graph Isomorphisms Read Chapter 1.2 Problems Chapter 1.1 #10,13,16,21,29,30 04/02 Walks, Cycles and Bipartite Graphs Read Chapter 1.3Problems Chapter 1.2 #2,8,10,17,20,38 04/05 Components, Cut-edges, Eulerian Graphs Problems Chapter 1.2 #11,27,30 04/16 04/07 Vertex Degrees and Degree Sequences Read Chapter 1.4Problems Chapter 1.3 #1,8,12,14,18,31 04/09 Directed Graphs Read Chapter 2.1Problems Chapter 1.4 #9,15,19 04/12 Eulerian Digraphs and Trees Read Chapter 2.2Problems Chapter 1.4 #26,27Problems Chapter 2.1 #2,6,19 04/23 04/13 Trees and Distance Problems Chapter 2.1 #11,23,27,32 04/14 Counting Trees and Prüfer Codes Read Chapter 2.3Problems Chapter 2.2 #1,7,8 04/16 Counting Spanning Trees and the Matrix Tree Theorem Problems Chapter 2.2 #12,15 04/30 04/19 Minimal Spanning Trees and Shortest Paths Read Chapter 3.1Problems Chapter 2.3 #2,3,16 04/21 Matchings Read Chapter 3.2Problems Chapter 3.1 #8,10,18,28 04/23 Hall's Theorem and Coverings Problems Chapter 3.1 #1,5,24 (See Example 3.1.2),26,29 05/07 04/26 Maximum Matchings Read Chapter 4.3Problems Chapter 3.2 #1,5,6 04/28 Maximum Weighted Matchings 04/30 Hungarian Algorithm Read Chapter 5.1Problems Chapter 4.3 #1,2,3 05/14 05/03 Network Flow Problems 05/05 Max-flow Min-cut Theorem Problems Chapter 4.3 #11,13,14 05/07 Vertex Colorings Read Chapter 5.2Problems Chapter 5.1 #1,12,14 05/21 05/10 Bounds on Chromatic Numbers and Mycielski's Construction Read Chapter 5.3Problems Chapter 5.1 #20,31,33Problems Chapter 5.2 #1,9 05/12 Chromatic Polynomials Read Chapter 6.1Problems Chapter 5.3 #1,3,5,7,10,11 05/28 05/17 Chordal Graphs Read Chapter 6.2Problems Chapter 5.3 #9,18,19,24Problems Chapter 6.1 #2,3 05/19 Planar Graphs Problems Chapter 6.1 #12,13,21,25 05/21 Euler's Formula and Kuratowski's Theorem Problems Chapter 6.1 #8,9,33 -/- 05/24 Five and Four Color Theorems Read Chapter 7.1Suggested Problems Chapter 6.2 #1,4,6,12 05/26 Line Graphs and Chromatic Index Read Chapter 7.2Suggested Problems Chapter 7.1 #1,3,5,8,11,12,18,24,26 05/28 Hamiltonian Cycles Suggested Problems Chapter 7.2 #1,2,3,7,8,10,12,17 06/02 Unsolved Problems in Graph Theory
* Reading assignments are to be completed by the next class period.

LaTeX

• A sample LaTeX file which produces the following typeset document once compiled.
• List Of Mathematical Symbols
• TeX Reference Card by J. H. Silverman
• Hypertext Help with LaTeX
• TeX FAQ
• Combinatorics.net LaTeX resources
• The Not So Short Introduction to LaTeX 2e - Tobias Oetiker et. al.
• Short Math Guide for LaTeX - Michael Downes