Extremal Graph Theory
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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
Compute , the maximum number of edges in an -vertex graph containing no single edge.
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comb-extrem-101All Combinatorics chaptersAbout these 124 questions
The extremal function ex(n,H): Mantel and Turán with proofs and the unique extremal graph, supersaturation and stability, Kővári–Sós–Turán and Erdős–Stone, and the regularity and removal lemmas behind Roth, Szemerédi and Green–Tao. This set covers the chapter Extremal Graph Theory in Combinatorics: 26 easy, 56 medium and 42 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- The Extremal Function and Mantel's Theorem — 14 questions
- Turán's Theorem and Zykov Symmetrisation — 14 questions
- Two Further Proofs: Induction and Weight Shifting — 13 questions
- Inside the Turán Graph — 13 questions
- Corollaries: Independence, Supersaturation, Stability — 13 questions
- Bipartite Forbidden Graphs and the Erdős–Stone Theorem — 15 questions
- Density in the Integers: Roth and Szemerédi — 14 questions
- Regularity, Removal and the Density Increment — 14 questions
- Green–Tao and the Reach of the Method — 14 questions