$Δ$-Y Moves and Partial Steiner Systems

RESUMO

We study graph systems generated by $\Delta$-Y and Y-$\Delta$ moves and prove that, for initial graphs of minimum degree at least $7$, $\Delta$-Y moves alone generate every reachable graph. As a consequence, for $n\ge 8$, the $\Delta$-Y system generated from the complete graph of $n$ vertices is canonically isomorphic as graded directed graphs to the space of partial Steiner systems on $n$ points.