Graph Theory, Spring 2014
Letters to students of Graph Theory

Welcome to the world of graph theory. Everything you learn here from this moment on will be new to you, just as it has been to those before you. The reason why I enjoyed this class is because previous knowledge is not necessary. You build your knowledge from the bottom. New terms will be defined for you. You will be introduced to different types of common graphs. Learn them and study them. Only then can you easily accept new knowledge and fuse it with your pre-existing one.

In the beginning, you will learn about points and lines, and common families of graphs such as the complete graph, or the wheel graph, and special graphs like the octahedral graph. In the beginning, there was so much input to remember. But review them over and over—you will start to learn and recognize them as quickly as they came.

You will be shown proofs for most of the theorems you learn, yet you will be asked to provide some proofs elsewhere. You will be asked to find statistics on these graphs such as the thickness of a given graph, its chromatic number, and its clique number. I too was overwhelmed at first, but apply these statistics to graphs. With practice, it will become second nature to you.

The key thing to remember is, "Do not be a passive learner". Those that listen and wait but do not seek, practice, and apply will not appreciate what they've learned. Instead, they will find themselves frustrated and falling behind. You are here to own what you learn. Review your notes the same night you wrote them down. Read the related sections in the book to reinforce your learning. Don't wait until the last moment to complete the homework assignments. Some will take a long time, but you will not regret how long you've worked on them—your efforts will only help you master your understanding. When you meet with your group, come prepared to talk about what solutions you've figured out, what progress you've made, or to ask what you didn't understand.

If there is one thing that this class will never do, it is this: It will never get you bored. The topics contain a wide variety of interesting questions. With many questions, I have told myself, "Oh, I'm not able to find the solution yet. I'll just try one more time." Instead, I can't put the question down until I've found the solution. It has become an addiction to answer it, and I come back thirsty for more. Your enthusiasm for graph theory will grow exponentially by the fun related games to graph theory such as the Puzzle Loop, the Shikaku, and the Planarity Game, and I am sure you will enjoy the Gale Shapley play on stable marriages as much as our class had.

As this semester is ending, I have come away with an appreciation for seeing how graph theory is not just points and lines, but can be seen as a way to describe, finding, and understand the connections between people on the social level and it's applications on a practical level with events such as transshipment and the assignments of medical schools. So, I wish you all a stimulating, fun, and successful semester in graph theory and in all your other classes. Best wishes!

A former graph theory student,

Knowing that I struggle with theory and proofs I knew this class was going to be a challenge for myself. With that here are a few things that I can recommend to you having a fresh start:

  • Professor Chris's notes are excellent so do write everything down. Everything he puts on the board will assist you in understanding the proofs in the book as well as the theorems you will need throughout the course.
  • Do not just memorize the theorems, really try and comprehend them and how they work. Don't be too concerned about knowing the proofs word for word, just understand the theorems themselves.
  • Colored pencils are a must when drawing graphs they will assist you in understanding if you can see the significant differences.
  • Take advantage of Professor Chris office hours he is very helpful and wants his students to understand the material.
  • Take his advice on working in groups on the assigned homework. It will only benefit you as the student to talk out the problems and assist each other in understanding the material. Professor Chris is a stickler on his homework grades and when working in groups I found to get a better grade as well as understanding when I did work with my classmates.
And most of all just enjoy the class!

Dear Incoming Student,

This upcoming semester you should expect to learn alot of interesting things. Graph theory is alot more than vertices and edges. It is computer networks, traffic patterns, and alot of useful and interesting things. Expect alot of homework, but the homework is a really helpful tool to practice what you have learned. I basically saw how little I really understood a lesson from the homework. It allowed me to practice these concepts and really think them through.

A tip for incoming students is to form a study group or at least work with someone who takes a completely different approach to the material. This way you can view the material from different angles, which is key when trying to find things in graphs. So stay on top of your homework and enjoy the semester.