Combinatorics is one of the core courses in the computer science major among national and international universities. It is also one of the most popular research topics in the theoretical computer science research field, with many applications on many aspects of computer science. Graph theory is one of the main topics in combinatorics. Considering the mathematical background of students, this course plans to take graph theory as the main topic, together with some specific applications of graph theory on other combinatorics fields.

The target of this course is to teach basic concepts, tools and common results of graph theory in combinatorics. The main contents include theoretical analysis, algorithms principles and their applications. For the 2021 fall semester, we will mainly talk about the basic properties of graphs, common structures like trees, common properties like connectivity, and common topics and matching and coloring. We will start with basic concepts, move on with more details, and talk about common algorithms. The students will understand basic principles, know common graph properties and master the mathematical foundation.