Rainbow Connectivity of Randomly Perturbed Graphs

Document Type

Presentation Abstract

Presentation Date

4-15-2022

Abstract

In this talk I will explore the following graph model: For an arbitrarily dense graph H, we create a graph G by adding m additional edges uniformly at random. We then edge-color G randomly with r colors. I will talk about what it means for a graph to be rainbow connected and show that with r ≥ 5 and m a large enough constant, G is rainbow connected with high probability. This was conjectured by Anastos and Frieze in 2019 and proven by József Balogh, Cory Palmer and myself. This talk will cover all of the concepts required to understand our result and survey the proof.

Additional Details

April 15, 2022 at 3:00 p.m. Math 103 & Zoom

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