discipline

Pure Math

subject

Extremal combinatorics

lecturers

Gyula Katona

credits

2

period

1, 3

curriculum

Turán's theorem and its applications. Non-bipartite excluded subgraphs.

Bipartite excluded subgraphs: paths, complete bipartite graphs.

Szemerédi's regularity lemma and its applications.

Turán-Ramsey type theorems.

Extremal hypergraph problems.

Sperner's theorem and applications, YBLM inequality. Erdős-Ko-Rado theorem. Permutation method, method of left-shift. Minimalizing the shadow. Star method. Algebraic methods for extremal set-systems.

Extremal problems for other partially ordered sets.

literature

L. Babai, P. Frankl: Linear algebra methods in combinatorics, Univ Chicago.

K. Engel: Sperner Theory, Encyclopedia of Maths. and its Appl., Cambridge Univ. Press, 1997.

Form of tuition

Lectures

mode of assessment

oral exam