Implementing Conflict Graph Java

Question

I am trying to create a program that decides whether or not a set of courses have conflicting times, and from those that do not, create the largest subset of courses. My idea is to create a graph with nodes being the courses and edges connecting the nodes being conflicts. I would then color each node with no two adjacent nodes having the same color. Then I would pick the subset of courses as the ones with the most frequent color. I know there are many different ways to represent graphs in Java, however, I have never created one before, and am wondering what approaches would be good to use in my case. OR would there a more efficient approach to this problem?

Answer 1

class Course {
    double startTime, endTime; //24-hour times
    String color;
    LinkedList<Course> conflictingCourses;

    boolean conflictsWith(Course otherCourse) {
        if (this.startTime > otherCourse.endTime || otherCourse.startTime > this.endTime)
            return false;
        return true;
    }
}

Go through all pairs of courses and see which pairs return true for conflictsWith. Then color them.