I'm facing difficulties in finding a representation for solving the following graph theory problem :
Two movies are considered related if they have the same director. Given a set of movies I need to find the longest playlist so that for each day exactly 2 related movies are to be watched and any two movies from different days can't be related.
I thought one solution could revolve around bipartite graphs and finding a maximum matching but I didn't get far this way.
Thank you for reading my question, any indication as to how I could solve this problem is greatly appreciated.
Edit: I've forgot to mention that a movie could have multiple directors (for example 2).