建立了期末补考安排的图论模型，并利用着色理论进行优化，给出求补考安排最少次数的一个方法。
In this paper, a graph theory model for make-up examination arrangement is established and the optimized solution to the model with painting theory is given.
同一学年内，累计不及格课程（经补考后）三门及三门以上者，应予留级。
Inside same school year, accumulative total fails course (after classics make-up examination) 3 person that reach 3 above, should grant fail to go up to the next grade.
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