We compare three lower bounds for the minimum cardinality of a multiway cut in a graph separating a given set S of terminals. The main result is a relatively short algorithmic proof for a simplified version of a min-max theorem of the first and the third authors asserting that the best of the three lower bounds is actually attainable if every circuit of the graph contains a terminal node. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 8]
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