Let $G = (V,E)$ be an undirected graph on $n$ vertices. Pick an ordering of the vertices, $\mathcal{O} = ( v_{i_1},v_{i_2},v_{i_3},\dots )$. Now from that ordering, create a sequence of subgraphs $(H_{k})_{k=1}^n$ where the subgraph $H_k$ is the induced subgraph from the first $k$ vertices in $\mathcal{O}$. For any subgraph $H_k$, define the "frontier" to be the number of vertices in $G \setminus H_k$ such that are adjacent to a vertex in $H_k$.
The problem: Which ordering $\mathcal{O}$ of vertices minimizes the maximum frontier over all subgraphs in the induced sequence of subgraphs?