The second of the three formulations looks very impractical  it says 

These conditions are not enough to characterize a tour even though the  are restricted to be integers in the interval

since sub-tours like those in Fig. 26-3-IV [omitted] also satisfy the conditions.  However, if so-called loop conditions like

are imposed as added constraints as required, these will rule out integer solutions which are not admissible.  

This is vague about how many of these "as required" there are, but it gives the impression that one of these has to be imposed for every possible invalid subtour, which gives a combinatorially large number of these loop conditions.

I'll take a look at the first one of Dantzig's.