CN-TST 2015 Problem 6

There are some players in a Ping Pong tournament, where every $2$ players play with each other at most once. Given: (1) Each player wins at least $a$ players, and loses to at least $b$ players. ( $a,b\geq 1$ ) (2) For any two players $A,B$ , there exist some players $P_1,...,P_k$ ( $k\geq 2$ ) (where $P_1=A$ , $P_k=B$ ), such that $P_i$ wins $P_{i+1}$ ( $i=1,2...,k-1$ ). Prove that there exist $a+b+1$ distinct players $Q_1,...Q_{a+b+1}$ , such that $Q_i$ wins $Q_{i+1}$ ( $i=1,...,a+b$ )