Problem. In chess tournament each player, from all $n$ players, played one game with every another player. Prove that it is possible to number all players with numbers from $1$ to $n$ in such way that every player has unique number and none of them lost the game against player with number greater by $1$.
My first association was that this tournament can be represented by directed clique and for example edge $\langle a,b \rangle$ means that player with number $a$ won the game against player with number $b$. Then what I need to prove is that vertices in every directed clique with $n$ vertices can be numbered in such way that there in no edge $\langle i+1, \ i \rangle$ for all $i=1,2,...,n-1$.
But it seems very hard, I don't know how to approach.
Or maybe it isn't the problem from graph theory, I don't know.