I've applied to three US universities (A, B, C) for PhD programs. Universities A and B offered me interviews on two separate weekends, which I accepted. I then made travel arrangements with Universities A and B for interviews.
I was then offered an interview with University C on the same date as my University A interview. I asked C for an alternate date, which happened to be the same weekend as my interview with B. I informed C of this and gave them a list of dates that I was free to interview but was told that those were the only two dates possible at University C.
I asked A and B about changing my interview date but was told that I could not since travel arrangements had already been made (through the university/a university-sponsored travel agency).
Universities A and B are both higher on my list than University C, so I've decided to decline University C's interview.
How can I do this politely? I don't want to burn any bridges with University C.