Extremal Combinatorics

Extremal set theory, Ramsey theory, and Turán-type problems.


foundation tier

Extremal Combinatorics. Extremal set theory, Ramsey theory, and Turán-type problems.

Foundations and canonical references

The standard treatments of extremal combinatorics approach the subject from complementary angles. Jukna, Extremal Combinatorics (2011) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Alon, The Probabilistic Method (2016) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for extremal combinatorics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2011
    Extremal Combinatorics
    jukna-2011
  • textbook · primary · 2016
    The Probabilistic Method
    alon-2016, spencer-2016

In context

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Explore

  1. 01

    Ramsey Theory

    Ramsey numbers, Hales–Jewett, and arithmetic Ramsey results.

  2. 02

    Turán-Type Problems

    Edge-maximal graphs and hypergraphs avoiding fixed substructures.

  3. 03

    Szemerédi Regularity Method

    Regularity lemma, removal lemmas, and graph limits.


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