Math 355: Graph Theory
(Credit Hours:Lecture Hours:Lab Hours)
Maps, graphs and digraphs, coloring problems, applications.
Desired Learning Outcomes
Minimal learning outcomes
Graphs, trees, pathes and cycles, connectedness, chromatic number, planarity conditions, genus of a graph, the Five Color Theorem. Students should also be aware of Kuratowsky's Theorem, and the Four Color Theorem. If there is time, it is good to do the proof of Kuratowski's Theorem.
Possible textbooks for this course include (but are not limited to):
- Graph Theory by Rusell Merris
- Applied Combinatorics by Alan Tucker (Chapters 1-4 on Graph Theory).
A good additional resource is An Introduction to Graph Theory by Douglas B. West, but the book is probably too encyclopedic to use as a main text.
Possible other topics include spectral theory of graphs.