Tounament has champion

30 Views Asked by At

Let $G(V,E)$ be a simple directed graph such that

• for each pair of vertices $u\neq v$, exactly one of the two edges $(u,v)$ or $(v,u)$ is in $E$

Prove that there is a vertex $s \in V$ such that for all vertex $v\neq s$,

• either $(s,v) \in E$,

• or there exists $u \in V$ such that $(s,u) \in E $and$ (u,v) \in E.$

I don't know how to prove it please give me some help to prove it.