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Is it true that every finite tournament is contained in some finite vertex-transitive tournament? If not, is it known which tournaments satisfy this property? This seems like a basic question, but I have not been able to find a relevant reference.

In a comment @bof claims that every finite tournament is contained in some finite cyclic tournament. Why is that?

Is it true that every tournament is contained in some vertex-transitive tournament? If not, is it known which tournaments satisfy this property? This seems like a basic question, but I have not been able to find a relevant reference.

Is it true that every finite tournament is contained in some finite vertex-transitive tournament? If not, is it known which tournaments satisfy this property? This seems like a basic question, but I have not been able to find a relevant reference.

In a comment @bof claims that every finite tournament is contained in some finite cyclic tournament. Why is that?

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Tournament contained in vertex transitive tournament

Is it true that every tournament is contained in some vertex-transitive tournament? If not, is it known which tournaments satisfy this property? This seems like a basic question, but I have not been able to find a relevant reference.