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Research seminar in Discrete Mathematics
Research seminar in Discrete Mathematics
The perturbation thresholds of degenerate graphs
The perturbation thresholds of degenerate graphs
Organizers
Jie Ma
, Benjamin Sudakov
Speaker
Jie Han
Time
Tuesday, March 17, 2026 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
The randomly perturbed model was introduced by Bohman, Frieze and Martin in 2003, which interpolates the Dirac-type problems on minimum degree conditions and the same subgraph containment problem in random graphs $G(n,p)$. In this talk we will briefly survey known results and explain our recent work on embedding degenerate graphs in the randomly perturbed model. Indeed, the threshold of d-degenerate graph containment is known to be $n^{-1/d}$, and we show that the randomly perturbed threshold is $n^{-1/d-o(1)}$, that is, we obtain a saving polynomial in n.
Speaker Intro
Jie Han obtained his PhD degree from Georgia State University (US) in 2015 under the supervision of Prof. Yi Zhao. He then held postdoc positions at the University of São Paulo and University of Birmingham, until he took a tenure-track position at the University of Rhode Island in 2018. He joined Beijing Institute of Technology as a full professor in 2022. His research interests include extremal graph theory and extremal combinatorics.