hopcroft-karp | Finds a maximum matching of a bipartite graph

I am trying to get a matching between two sets of vertices, one represents meets between two teams and the other time slots when the meets could happen. The adjacency map represents both teams' availability to meet at any given time slot. This would be bipartite matching. The problem is that I want to constraint this so that any team will not be assigned to consecutive time slots, more specifically to time slots in two consecutive days.

So, I've tried adding a check right before adding an edge to the match, at the end of the augmenting path, that checks the previous day's and following day's time slots, if they have been matched to a meet with any of the teams in the meet about to match. I tried it with Hopcroft-Karp and with DFS. It didn't work.

Is this not bipartite matching anymore?

Any help will be greatly appreciated.

EDIT:

As suggested in the answer below, I am trying to implement this as an integer linear program. The following code is heavily based on the example from Google OR-tools on assignment matching As it is, it seems to work correctly for matching, but without my specified constraint.