Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, March 16, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Stefan Glock

Long induced paths in sparse random graphs

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.

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