About one family of exact 2-extensions of tournaments

Exact extensions were introduced by Harary and Hayes in 1996. Exact extensions are special case of minimal extensions of graphs and closely related to fault tolerance modeling. Only three families of graphs wich have exact $k$-extensions for every $k>0$ are known. In this paper we introduce new family of tournaments that have exact 1- and 2-extensions, but have no 3-extension.