Graph Theory and Additive Combinatorics (MIT 18.225)
by Yufei Zhao · MIT OpenCourseWare
Classical and modern results linking graph theory and additive combinatorics: Turán-type extremal problems, Szemerédi's regularity lemma, pseudorandom graphs, graph limits, Roth's theorem and Freiman's theorem, plus open problems. 26 lecture videos, lecture notes, Zhao's open textbook and problem sets.
More resources on Extremal Graph Theory
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Graph Theory and Additive Combinatorics
Explore graph theory and additive combinatorics! This course covers key concepts and applications in graphs & digraphs.
Diestel Graph Theory
Official site for Reinhard Diestel's Springer graduate text, where the main text is readable free online and paid eBook editions add the full apparatus. It covers matching, connectivity, planarity, colouring, flows, extremal theory, and minors.
Extremal Graph and Hypergraph Theory: With Ramsey Theory
Cambridge Studies in Advanced Mathematics text covering Turán-type problems for graphs and hypergraphs and Ramsey theory, using probabilistic and algebraic methods, with complete proofs of recent results on sunflowers and off-diagonal and geometric Ramsey numbers. Readers can follow and apply current research techniques.
The History of Degenerate (Bipartite) Extremal Graph Problems
Every textbook treatment stops where Erdős-Stone stops being informative; this is the standard reference for what happens after that, and it is the survey working researchers cite. Ninety-seven-page survey of extremal graph problems where the forbidden graph is bipartite, the degenerate case Erdős-Stone leaves open. Covers Kővári-Sós-Turán, norm graphs, finite-geometry constructions, and the main conjectures, with historical context.
Extremal Graph Theory — Cambridge Part III Course Notes
Fifteen lecture notes from David Conlon's Cambridge Part III course, running from Mantel's and Turán's theorems through Erdős-Stone-Simonovits, the regularity lemma, dependent random choice, Bondy-Simonovits and hypergraph Turán problems. Two example sheets with full solutions.