Matrix characteristics of integer-guaranteed and integer-friendly formulations. You have read about linear programming formulations that guarantee integer or all zero-one solutions, and you have read about formulations that "favor" integer or zero-one solutions.
The latter are the formulations we called integer-friendly.
Look back at the formulations in these two categories and see if you can find features in common in them.
Specifically, look al the coefficients (elements) of the constraint matrix and observe their values. Look as well at right-hand sides of the constraints and observe their values.
(You are unlikely lo find commonality in the number of elements in the columns.)
What do the two kinds of problems have in common?