prevent time collision in N Course initiation for M Student

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Hypothesis: we have n courses and m students. we decide to initiate a sample course program named Math123. how many Time Unit do we need to Students will not have two different courses at the same time. the reason is to prevent time collision.

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If I’m interpreting this correctly, we form the graph on the classes where two classes are adjacent if they have a common student. Then you want to know the chromatic number of this graph.