| Abstract |
The Grid Minor Theorem by Robertson and Seymour is one of the most important results in structural graph theory. In recent years, there has been growing interest in exploring an induced analogue of this theorem. In this talk, we prove that for all positive integers $k$ and $d$, the class of $K_{1,d}$-free graphs not containing the $k$-ladder or the $k$-wheel as an induced minor has a bounded tree-independence number. These two graphs can be considered as strong evidence for existence of a grid as an induced minor. Our proof uses a generalization of the concept of brambles for tree-independence number. This is based on joint work with Claire Hilaire, Martin Milanič, and Sebastian Wiederrecht. |
