Liana Yepremyan, Emory University
Authors: Julia Boettcher, Peter Allen
2023 AWM Research Symposium
Extremal and Probabilistic Combinatorics [Organized by Jinyoung Park and Corrine Yap]
We show that for every \gamma>0 if p>> \frac{\log{n}}{n^{1-gamma}} then a.a.s. any o(pn)-bounded edge-coloured $G(n,p)$ satisfies the following. If $H$ is an n-vertex subgraph of G(n,p) with minimum degree at least p/2+o(n) then G has a rainbow Hamiltonian cycle. Our method largely relies on various probabilistic tools and employs absorption ideas and regularity. This is joint work with Peter Allen and Julia Boettcher.