Combinatorics, Graph Theory, Matroid Theory
Recommended Texts or Study Materials
- Matroid Theory, Oxley.
- Graph Theory, Diestel.
- Graph Theory, Douglas West.
- Notes for any course given by Guoli.
Foundational Tools/Techniques/Ideas:
Topics
- Graph Theory
- Matroid Theory
- Linear Algebra
- Linear Programs
Techniques and Tools
- Induction
- Minimal counterexamples
- Counting/enumeration
- Graph and Matroid operations (edge deletion, edge contraction, vertex deletion, etc.)
Common Advisors and Committee Members
| Advisor | Committee Member 1 | Committee Member 2 |
|---|---|---|
| Dr. Guoli Ding | Dr. James Oxley | Dr. Zhiyu Wang |
| Dr. James Oxley | Dr. Guoli Ding | Dr. Zhiyu Wang |
Previously asked questions
- Give an example of a non-representable matroid.
- Linear program solutions as they apply to matroid polytopes.
- Is matroid \( M(G) \) graphic? Why or why not?
- What is an example of a (non)-representable matroid? Prove it.
- Coloring and flows on a given graph.
- Coloring and flow conjectures and theorems.
- Connectivity of Matroids and Graphs. What about related graphs through matroid/graph operations?