Cutwidth

The cutwidth of an undirected graph ${\displaystyle G=(V,E)}$ is the smallest integer ${\displaystyle k}$ with the following property: there is an ordering ${\displaystyle (v_{1},\ldots ,v_{n})}$ of the vertices of ${\displaystyle G}$, such that for every ${\displaystyle l=1,\ldots ,n-1}$, there are at most ${\displaystyle k}$ edges with one endpoint in ${\displaystyle \{v_{1},\ldots ,v_{l}\}}$ and the other endpoint in ${\displaystyle \{v_{l+1},\ldots ,v_{n}\}}$.[1] [2]