Consider a bipartite graph $G=(U, V, E)$. Each $v \in V$ represents a soccer team, and each $u \in U$ represents a mini-tournament needs to be scheduled.
If $u_i$ and $u_j$ share no common neighbor, these two tournament can be scheduled on the same day. Similarly, one can schedule multiple tournaments in one day if there is no such conflict.
Is there a way to compute the minimum number of days required to complete all the tournaments and the corresponding scheduling?