A binary structure $S$ has the pigeonhole property ($\mathcal{P}$) if every finite partition of $S$ induces a block isomorphic to $S$. We classify all countable tournaments with ($\mathcal{P}$); the class of orders with ($\mathcal{P}$) is completely classified.

Keywords:

pigeonhole property, tournament, order pigeonhole property, tournament, order

MSC Classifications:

05C20, 03C15 show english descriptions Directed graphs (digraphs), tournaments
Denumerable structures 05C20 - Directed graphs (digraphs), tournaments
03C15 - Denumerable structures

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