- Series
- Combinatorics Seminar
- Time
- Friday, October 10, 2025 - 3:15pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Corrine Yap – Georgia Institute of Technology – cyap35@gatech.edu – https://corrineyap.com/
- Organizer
- Jiaxi Nie
Given a feasible degree sequence D, we consider the uniform distribution over all graphs with degree sequence D. In 1995, Molloy and Reed gave a criterion for determining the existence of a giant (i.e. linear in n) component for degree sequences satisfying certain technical conditions; in 2018, Joos, Perarnau, Rautenbach, and Reed gave a refined result that applies to essentially all feasible D. In this talk, we work in the "supercritical" regime and uncover the precise structure of the giant component when it exists, obtaining bounds on the diameter and mixing time of the random walk on the giant which are tight up to polylogarithmic factors. Our techniques involve a variation of core-kernel reduction and analysis of the switch Markov chain. Joint work with Louigi Addario-Berry and Bruce Reed.