In: Advanced Math
A round-robin tournament involving n plays is modeled with digraph D where, for every two distinct vertices (players) u and v, either (u,v) is an edge (player u defeats player v) or (v,u) is an edge (player v defeats play u). Prove that if D is acyclic, i.e., no directed cycles, then there always exists a player who has defeated everyone (out-degree is n – 1) and a player who has lost to everyone (in-degree is n – 1).