4 problems

Let $G$ be a graph of tree-depth $k$, meaning that $k$ is the least number of labels in a vertex ranking of $G$ such that every path joining two vertices with the same label contai…

Every-critical-graph conjecture. Every critical graph is 1-unique.

Let $G$ be a critical graph, meaning that it has tree-depth $k$ for some $k$ and every proper minor of $G$ has smaller tree-depth. A graph is 1-unique if, for every vertex $v$ of…

Let $G$ be a critical graph with tree-depth $k$, meaning that $G$ has tree-depth $k$ and every proper minor of $G$ has smaller tree-depth. The maximum-degree conjecture. The maximu…