Graph Theory and Combinatorics Seminar
- Sponsor
- Department of Mathematics
- Speaker
- Igor Araujo
- Contact
- Abhishek Dhawan
- adhawan2@illinois.edu
- Views
- 3
- Originating Calendar
- Mathematics Seminar Series: Combinatorics
Speaker: Igor Araujo (UIUC)
Title: The third power of a Hamilton cycle in randomly perturbed graphs
Abstract: Answering a question of Böttcher, Parczyk, Sgueglia, and Skokan, we fully determine the randomly perturbed threshold for the containment of the third power of a Hamilton cycle. This provides the first example of a randomly perturbed threshold exhibiting an uncountable number of jumps. Our proof combines the Spread Blow-Up Lemma of Nenadov and Pham with a spread distribution on (not necessarily perfect) matchings, inspired by the framework of Pham, Sah, Sawhney, and Simkin. We expect that these techniques extend to determining randomly perturbed thresholds for higher powers of Hamilton cycles and for many other spanning structures, and hence are of independent interest.
In this talk, we discuss the randomly perturbed graph model and survey results on powers of Hamilton cycles in this setting. The talk is based on joint work with Abhishek Methuku and Aaditya Raghavan.