Talk information

Date: Sunday, November 10, 2024
Time: 10:10–11:00
Place: Schreiber 309
Speaker: Eden Kuperwasser (Tel Aviv University)
Title: On the anti-Ramsey threshold

Abstract:

We say that a graph $G$ is anti-Ramsey for a graph $H$ if any proper edge-colouring of $G$ yields a rainbow copy of $H$, i.e. a copy of $H$ whose edges all receive different colours. In this talk we will determine the threshold at which the binomial random graph becomes anti-Ramsey for any fixed graph $H$, given that $H$ is sufficiently dense. This extends the previously known cases where $H$ is a clique, a cycle, or close to a regular graph with sufficiently many vertices. Our proof employs a graph decomposition lemma in the style of the Nine Dragon Tree theorem that may be of independent interest.