Instructor: Prof. Linyuan Lu
Office: LC 400I, Email: lu@math.sc.edu
Office hours: TTh 9:30AM- 11:00AM or by appointment.
Lecture time: Tuesday & Thursday 12:30AM- 1:45PM, LC 303B
Credit Hours: 3
Prerequisite: Some background in graph theory
Reference textbook: Extremal Graph Theory, by Bela Bollobas, Academic Press Inc.
Overview: Extremal graph theory was initiated by Tur\'an in 1940, and developed by Paul Erdos and many others through many papers, lectures, and uncoutably many problems. In extremal graph theory, one is interested in the relations between the various graph invariants, such as order, size, connectivity, minimum degree, maximum degree, chromatic number, diameter, and also in the values of these invariants which ensure that the graph has certain properties. We will also consider extremal problems in hypergraphs and finite sets.
Learning Outcomes: Students will state classical theorems in the extremal graph theory. They will be able to read research papers and present results in the class. They will combine methods learned from this course and practice them at new problems. Students will demonstrate their problem-solving skills through homework, an exam, and a final project.
Subject Material: We shall cover the selected material presented in the textbook and other supplemental marterial for selected papers.
Assessment: The assessment consists of homeworks, an exam and a take-home final exam. Homeworks will normally be assigned every other week.
Grading: The breakup grades are homework 50%, midterm 20%, and final 30%.