The next meeting of the Mathematical Foundations of Informatics seminar will be held on November 10, 2023, at 2 p.m. in Room 478 of the Institute of Mathematics and Informatics.

A talk on:

## On induced \(C_4\)-free graphs with high average degree

**Antonio Girao**.

**Abstract**. A long-standing conjecture of Thomassen from the 80’s states that every graph with sufficiently high average degree contains a subgraph with high girth and still preserving large enough average degree. This conjecture has only been resolved in the early 2000’s by Kühn and Osthus in the first non-trivial case i.e. they showed that for every \(k\), there is \(f(k)\) such the every graph with average degree at least \(f(k)\) contains a subgraph which is \(C_4\)-free with average degree \(k\).

**Antonio Girao **is a post-doctoral fellow at the University of Oxford under the supervision of Prof. Alex Scott. Prior to this position, Antonio worked as a postdoctoral fellow at the University of Heidelberg under the supervision of Prof. Felix Yoos and at the University of Birmingham under the supervision of Prof. Daniela Kuhn and Prof. Derek Ostus. He defended his PhD at the University of Cambridge under the supervision of Prof. Bela Bolobas in 2018.