The cs department has six committees, each meeting once a month. the committees are:

alumni relations : fischer, solomon, vernon
curriculum : dewitt, goodman, vernon
facilities : fischer, meyer, solomon
graduate admissions : dewitt, naughton, vernon
graduate advising : goodman, solomon, vernon
undergraduate advising : dewitt, meyer, naughton

what is the minimum number of different meeting times needed to ensure that no member is scheduled to attend two meetings at the same time? make sure to justify your answer. to receive full credit your answer must use graph coloring.