■ Block 01 / research
Research
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
How large can a discrete structure be without containing a forbidden pattern? Ramsey theory, Turán problems and set systems, attacked mostly by random constructions, entropy and iterative algorithms.
Minors, tree-width and the Robertson–Seymour theory; the extremal density of K_t-minor-free graphs; and colouring by excluded minors, from the Four Colour Theorem to Hadwiger's conjecture.
Proving existence by random construction: moments, alteration, the Lovász Local Lemma, martingale and Talagrand concentration, entropy and hypergraph containers, with uses in combinatorics and complexity.