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Given $F_1,F_2,..,F_n$ as set of final exams of subjects taken by students $S_1,..,S_k$ in h slots such that no student takes two exams in a single slot.Here the objective is to maximize the number of exams taken by a student in a single slot.

I reduced the problem to graph coloring problem where the nodes of the graph are the final exams of subjects and edges would be the students. The chromatic number of graph would be h.

But I am not sure how to represent edges as they can me multiple also as same exams are taken by multiple students and would it have any impact on constraint satisfaction formulation?

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