Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 19, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Rajko Nenadov

On Counting Lemma for sparse graphs (Master thesis)

Szemeredi's regularity lemma, together with the corresponding embedding and counting lemmas, is an important tool in modern graph theory. However, because of the underlying definition of regularity it is only helpful when one is dealing with dense graphs, that is, graphs of density cn^2 for some constant c. In 1997, Kohayakawa and Rödl introduced a modification of regularity that makes it applicable to the certain class of graphs with density o(n^2), and Kohayakawa, Luczak and Rödl conjectured a corresponding embedding lemma. The embedding conjecture has been proven only recently, and using some stronger assumptions the counting version was derived. We show that the counting lemma for some special cases, namely K₄, K₅ and K₆, can be proven using the same setup as the embedding conjecture without any additional assumptions.

Thesis supervised by Angelika Steger.

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