In the Dantzig$-$Fulkerson$-$Johnson $($DFJ$)$ formulation of the TSP$,$ the core LP has a degree constraint,

${\displaystyle \underset{i=1}{\overset{j-1}{}}}{x}_{i,j}+{\displaystyle \underset{i=j+1}{\overset{n}{}}}{x}_{j,i}=2,$

for each city $1jn.$ If we solve the core LP and find a set of cities Ssube$\{1,$dots,$n\}$ that forms a subtour, we then add a subtour elimination constraint to the core. Bill Cook uses inequalities like

${\displaystyle \underset{?}{\overset{?}{}}}$

to eliminate subtours. Another option is to use inequalities like

$Sv{\displaystyle \underset{?}{\overset{?}{}}}(x_e$:ein$(\{v\}))=2{\displaystyle \underset{?}{\overset{?}{}}}(x_e$:ein$(S))2{\displaystyle \underset{?}{\overset{?}{}}}(x_e$:einE$(S))|S|-1(\{v\})v,(S)SE(S)S{\displaystyle \underset{?}{\overset{?}{}}}$