Metric small cancellation condition ($C^{\prime }(\lambda )$)

The condition $C^{\prime }(\lambda )$ requires that every piece in small cancellation theory occurring in a cell boundary have length strictly less than $\lambda$ times that cell's perimeter. Length counts edges. For $\lambda =1/6$, an inner path made of at most three pieces has length strictly less than half the perimeter, so the complementary outer path is strictly longer. The attaching paths are combinatorial immersions and the piece convention is part of the chosen presentation or polygonal complex.