each of the following problems can be solved by finding either the chromatic number of a graph or the chromatic index of a graph. for each problem, say whether you should find a proper coloring of the vertices or of the edges of the graph to solve the problem. note: you likely don't have enough information to actually solve the problem, but this is okay. just say in principle whether this is an edge-coloring or vertex-coloring application. edges 1. at the world tic-tac-toe championship, each player must play against 7 other players. new games start every hour. how many hours will the tournament take? vertices 2. your teacher wants to have different versions of the final exam so that no students that are seated within 4 feet of each other have the same version of the exam. how many versions are needed? edges 3. the math department wants to schedule common, day-long midterm exams over spring break, but obviously a student in two classes has to have their exams for those classes on different days (but this is the only problem with this plan). how many days are needed for exams? edges 4. 5 students will interview with 4 companies for internships at a job fair. how many time slots are needed for interviews?