= Server connectivity under component failures
{title2=$k_{\max}=\lambda-1$}
To find the smallest link failure set separating a client from every server, add a common sink with sufficiently large-capacity server arcs and give original links unit capacities in both directions. The <max-flow min-cut theorem> identifies the minimum failure count $\lambda$. Unit-capacity <vertex splitting> also charges intermediary node failures. The network tolerates fewer than $\lambda$ failures and fails for some set of $\lambda$ failures. This concerns connection to at least one server, not separate connectivity to each server.
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