Let S be a planar point set in general position, and let $$\mathcal {P}(S)$$ the of all plane straight-line paths with vertex S. A flip on path $$P \in \mathcal is operation replacing an edge e P another f to obtain new valid from . It long-standing open question whether for every given S, can transformed into any other by sequence flips. To achieve better understanding this question, we show t...