Long induced paths in sparse random graphs (rescheduled from Feb 22)

Abstract: The study of induced trees in random graphs was initiated by Erdős and Palka in the 80s. Many interesting questions remain unanswered, especially in the sparse case when the average degree is constant. For instance: what is the length of a longest induced path?

Natural algorithms produce an induced path of length roughly half the conjectured optimal value, which has not been improved in the last 30 years.

We show that one can do better than that, which answers a question of Fernandez de la Vega. Unfortunately, we only get halfway towards the upper bound. We will explain the main ideas and explore possible ways to close the remaining gap.

combinatoricsprobability

Audience: researchers in the topic

Extremal and probabilistic combinatorics webinar

Series comments: We've added a password: concatenate the 6 first prime numbers (hence obtaining an 8-digit password).