The existence of a source and sink
Task number: 4457
HintConsider the longest path.
The initial vertex \(s\) of the longest oriented path must be a source: if it was not, there is an edge \((x,s)\) from some vertex \(x\). If \(x\) lies on the path, there is a cycle in the graph; if it does not lie on the path, the path can be extended by the edge \((x,s)\) so that it was not the longest.
We use an analogous argument to prove that the last vertex of the path is the sink.