@AishesChayil:
I think that you may be mixing up the obligation to divorce with there being a death penalty (which requires witnesses and a warning) or her forfeiting her kesubah (which needs witnesses, but not a warning). If the husband knows that his wife is being unfaithful, even without any witnesses, he has to divorce her (although I have been involved with cases where the psak was that if the husband does not know, there is no chiyuv to tell him). And out of curiosity, where did you hear that a Kohen has to divorce her even based on a rumor?