Suppose I run a relaxation of an MIP. If my result is all integers, I have achieved the same min/max that the MIP would achieve. However, what can I say if some portion of my result is integer?
If half my decision variables come out integer, does that mean that those specific variables would/should keep the same integer value for the MIP result? Does it depend on the problem? Is it different if I'm using boolean variables only?
I'm not sure what to look for to find research on this topic. What are the distinct keywords? What is the existing research on this topic?