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For any $k$, the class of graphs of treewidth at most $k$ can be characterized by a finite set of forbidden minors. For treewidth $1$ and $2$, the set is of size $1$. Then for treewidth $3$, the set ...

For any integer $n$, let ${\cal G}_n$ denote the set of simple, undirected graphs $G = (V, E)$ where $V = \{1,\ldots,n\}$. The Hadwiger number $\eta(G)$ of a finite graph $G$ is the maximum integer $m$...

If $G$ is a finite, simple, undirected graph, its Hadwiger number $\eta(G)$ is the maximum integer $n$ such that $K_n$ is a minor of $G$. Given any integer $k>0$ let $E_k$ be the expected value of ...