Can anyone assist me to find out what should be the ILP formulation of a case when I try to label vertices by say $0$, $1$ and $2$ and want the subgraph of graph $(V,E)$ made by same vertex set but edge set being those which have at least one end point as $1$ or $2$, to be connected. I don't need objective functions, just want to know how to show this as a constraint.
Imposing contiguity constraints in political districting models, by Hamidreza Validi, Austin Buchanan, and Eugene Lykhovyd, is a very recent paper (January 27, 2020) that provides a good survey of integer linear programming models for connectivity in the context of political districting.
This paper helped me understand a lot on connectivity of subgraphs. A must look for those seeking an answer.