Don't lock it yet. I still have to prove the converse...
Before I begin, I'm proposing that we advance the terminology and notation a little bit. Instead of referring to u > v as a directed edge of T, I would like to refer to (u, v) as an arc of T.
Any objections?
Since there seems to be sufficient interest...
Suppose T is a tournament that contains no cycles, and chose arcs (u, v) and (v, w) from T. Obviously (w, u) cannot be an arc of T, as that would be a cycle and hence a contradiction. Therefore, (u, w) is an arc of T, and T is transitive.
Don't lock it yet. I still have to prove the converse...
Before I begin, I'm proposing that we advance the terminology and notation a little bit. Instead of referring to u > v as a directed edge of T, I would like to refer to (u, v) as an arc of T.
Any objections?
Since there seems to be sufficient interest...
Suppose T is a tournament that contains no cycles, and chose arcs (u, v) and (v, w) from T. Obviously (w, u) cannot be an arc of T, as that would be a cycle and hence a contradiction. Therefore, (u, w) is an arc of T, and T is transitive.
By posting anything after this you agree to all of the following:
a) David Hasselhoff should be the the next President of the Unites States;
b) Langdon should drop the forums from DPC. Pictures only from now on (with exception of the banning thread); and
c) One night with George Michael (doesn't matter if you're a girl or gay guy).
