Kombinatorika a grafy 3

Přednáška: Čtvrtek 15:40–17:10 v S3. Cvičení: Čtvrtek 14:00–15:30 v S3.

Podmínky získání zápočtu: za řešení domácích úkolů a aktivní účast na cvičeních, více info u cvičícího (Guillaume Aubian).

Plán přednášek
• 5.10: Graph classes closed under subgraphs/minors/...: Lecture notes: Introduction and Section 1, excluding the parts on treedepth.
• 12.10.: Minor-closed classes, Hadwiger's conjecture, average degrees: Lecture notes: Everything except for section 4; we only started the proof from section 5, we will finish it in the next lecture.
• 19.10.: Topological minors, Hajós' conjecture, linkedness: Lecture notes: Sections 2 and 3; statement of Lemma 2 from these notes (the proof will be done in the next lecture).
• 26.10.: The proof of Lemma 2 left over from the previous lecture.
• 2.11.: Cancelled (sporting day).
• 9.11.: Tree decompositions and treewidth, brambles. Definition and Corollary 9 (with slightly different proof) from these lecture notes, section 1 from these. The results on brambles are only in the Czech notes (till the end of Section 1).
• 16.11. Grid minors, ladder lemma and Erdős-Pósa theorem. Lecture notes, sections 3 and 4.
• 23.11.: List coloring and polynomial method: Lecture notes. We got up to Theorem 6, the rest will be finished in the next lesson.
• 30.11.: Finished the Alon-Tarsi list coloring argument. VC-dimension (definition, examples, statement of Theorem 3 from the lecture notes.
• 7.12.: Application of VC-dimension to design of approximation algorithms (Corollary 4 from the lecture notes). Spanning trees (everything from the lecture notes).
• 14.12.: Epsilon-regular pairs and the formulation of the Regularity Lemma. Lecture notes.
• 21.12. Applications of the Regularity Lemma. Lecture notes.
• 4.1.: Arithmetic Ramsey theory. Section 1 from the lecture notes.
• 11.1.: Proof of Regularity lemma. Lecture notes.
Obsah přednášek a poznámky
Další zdroje

Domácí úkoly (rok 2016):

Domácí úkoly (rok 2015):

Anglické verze poznámek (rok 2014):