Problem

There are two types of professional wrestlers: $$babyfaces$($good guys$)$ and $$heels$($bad guys$).$ Between any pair of

professional wrestlers, there may or may not be a rivalry. Suppose we have n professional wrestlers and we have a list of

r pairs of wrestlers for which there are rivalries. Give an O$($n $+$ r$)-$time algorithm that determines whether it is possible to

designate some of the wrestlers as babyfaces and the remainder as heels such that each rivalry is between a babyface and a

heel. If it is possible to perform such a designation, your algorithm should produce it$.$