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This is a follow-up to an earlier question.

Suppose you start at a given score sequence, and ask "how many tournaments, up to isomorphism, have this score sequence?" For $\{0, 1, 2, ..., n-1\}$ the answer is $1$, and for a few other sequences.

If we set aside the transitive tournaments for a moment, one can ask are these other sequences (for whom the answer is $1$)?

According to the theorem that tournaments are made up of a transitive string of strong components, we are looking for strong tournaments such that no other tournament exists having the same degree sequence.

The only examples seem to be the regular tournaments ($\{0\}, \{1, 1, 1\}, \{2, 2, 2, 2, 2\}$ etc.). And also $\{1, 1, 2, 2\}$. Are these the only ones? What others are there?


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Why not link to the earlier question? – joriki Oct 30 '12 at 23:31
Not sure how to do that. – John Smith Nov 1 '12 at 18:47
There's an edit link directly underneath the question. If you click it you'll get a text area in which you can edit the question. If you select text and click on the link icon directly above the text area, you can enter a URL to link the selected text to. – joriki Nov 1 '12 at 22:57
Are the regular tournaments unique up to isomorphism? – Tássio Feb 19 at 12:41

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