= Cut feasibility for a rearrangeable triangle
{title2=$n_{12}+n_{13}\leq C_{12}+C_{13}$}
The three cyclic versions of this inequality are necessary and sufficient for routing unit calls on a triangle with complete instantaneous rearrangement. Necessity counts endpoint calls through a node cut. For sufficiency, at most one call count can exceed its direct-link capacity, since any two such excesses would violate their common endpoint cut. Route that one excess along the two other links; the two relevant cut inequalities guarantee room there. This gives an exact reduction to a <loss network> with a virtual resource at each node.
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