5 problems

For a graph class $\mathcal{G}$, let $\operatorname{obs}(\mathcal{G})$ denote its minor obstruction set. For a class property $\mathbb{C}$, let $\operatorname{cobs}(\mathbb{C})$ be…

For a graph class $\mathcal{G}$, let $\operatorname{obs}(\mathcal{G})$ denote its minor obstruction set. For a class property $\mathbb{C}$, let $\operatorname{cobs}(\mathbb{C})$ be…

Let $\mathcal{H}$ be a graph class, let $h$ denote the relevant size parameter for $\mathcal{H}$, and let $\ell$ be the linkage function. The paper obtains the bound … for the size…

Ubiquity conjecture. If $\mathsf{p}$ has a finite universal obstruction $\mathfrak{Z}_{\mathcal{H}}$, then

A graph is $n$-apex if deleting $n$ or fewer vertices results in a planar graph. A graph is a minor of another graph if it can be obtained by contracting edges in a subgraph. Let…