3 problems

Let $p,q\geqslant 1$ be integers. Define $\ell(p,q)$ to be the minimum integer such that every graph $G$ with treewidth at least $\ell(p,q)$ contains pairwise disjoint connected su…

A graph class is hereditary if it is closed under taking induced subgraphs. The tree-independence number of a graph is the minimum, over its tree-decompositions, of the largest ind…

Polynomial grid-minor conjecture. The function