Who was Timothy Shepard and why was he looking for Dally Winston in The Outsiders?

Timothy Shephard is the leader of another greaser gang.  He demands more discipline and organization of his "outfit" than Darry's gang, which more like a group of childhood friends.  Tim Shepherd "enjoys being a hood", and his boys can be formidable.  Tim's gang can be counted on to back up Darry's if necessary, and Tim is good friends with Dally, even though they fight.

Tim Shepherd is looking for Dally in Chapter 2 because someone slashed the tires on his car, and Tim's brother Curly "spotted Dally doing it".  Two-Bit observes nonchalantly that "skin fighting", or tangling without weapons, "isn't rough...it blows off steam better than anything", and that if Dally doesn't "pull a blade", Tim will fight fair.  Two-Bit figures that if it's a fair fight, Dally "deserves whatever he gets", because it takes a lot of hard work to get the money to replace tires, and because he got caught.  Two-Bit says, "Dally was getting kicks.  He got caught.  He pays up.  No sweat".