. Let be the last layer created, that is, the lowest value for such that .

The graph is then re-expressed as a series of digraphs where each and where is the contraction of all previous levels into a single vertex. Because every dipath appears in at most two consecutive layers, and becauseeach is formed by two consecutive layers, every dipath in appears in its entirety in at least one (and no more than 2 consecutive such graphs)

For each , three separators are identified which, when removed, break the graph into three

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