Difficult# Determining if a Graph is Bipartite

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For a group project, you and your partner are given a list of seminars that you need to write summaries on. In order to do this, one of you must go to each seminar in order to write a summary about it. However, some of the seminars overlap in time and you are not allowed to leave a seminar early or come in late.

Therefore, you need to find a way to divide up the seminars such that neither of you is given two overlapping seminars but between the both of you, every seminar is attended. Assume the list of seminars allows you to do this.

Which of the following methods is the most efficient way to do this that will always return the correct answer?