= Cyclic stability of a digraph order
{title2=$\alpha(\mathcal C)$}
= Cyclic stability
{synonym}
The cyclic stability is the largest size of an <independent set> appearing consecutively in a representative of a <coherent cyclic order of a digraph>. It is at most the ordinary <independence number>. A set with no forward path between its distinct vertices can be moved into a consecutive block by swapping nonadjacent vertices. Choose a representative minimizing the span of the set; a vertex in a gap can be moved left or right past the block, contradicting minimality unless there are no gaps.
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