Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, February 23, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Miloš Trujić

Sparse blow-up lemma for cycles

Szemerédi's regularity lemma and the blow-up lemma of Komlós, Sárközy, and Szemerédi are some of the most powerful tools in modern combinatorics, which lead to many deep and beautiful results. The biggest 'flaw' of these tools is that they are not directly applicable in sparse settings. Nevertheless, in 2016, Allen, Böttcher, Hàn, Kohayakawa, and Person provided a first analog of the blow-up lemma applicable to sparse graphs. In this talk, we present a specific variant of the sparse blow-up lemma designed for cycles improving the result of previously mentioned authors. As an application of our blow-up lemma we resolve a question of Nenadov and Škorić regarding resilience of cycle factors in sparse random graphs.

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