Sufficient conditions for relaxed integer programs to have integer solutions.

Question

Suppose we are given an integer program and we remove the integrality constraints to get a relaxed linear program. Are there a set of sufficient conditions on the form of the linear program, (e.g. conditions on the coefficients in the constraints), that guarantee that the solution to the relaxed linear program is integral?

Answer 1

(I wish I could simply comment this instead of doing an answer, but) Here is a Wikipedia article you might want to read: https://en.wikipedia.org/wiki/Linear_programming_relaxation