Given a tournament T, a subset M of V(T) is a module of T if for any \(x,y\in M\) and \(v\in V(T)\) such that \(xv,vy\in A(T)\) , we have \(v\in M\) . A tournament T is decomposable if it admits a module M such that \(1<|M|<|V(T)|\) . Two tournaments T and U are \(\{-1,3\}\) -hypomorphic if \(T-v\simeq U-v\) for each \(v\in V(T)\) , and \(T[X]\simeq U[X]\) for each \(X\subseteq V(T)\) such that \(|X|=3\) . A tournament T is \(\{-1,3\}\) -reconstructible if every tournament \(\{-1,3\}\) -hypomorphic to T is isomorphic to T. We provide sufficient conditions for a decomposable tournament to be \(\{-1,3\}\) -reconstructible. For instance, we establish that a tournament, which admits a proper module of size \(\ge 3\) , is \(\{-1,3\}\) -reconstructible.
