For example, a maximal path for S 1 and S 2 is P = e → g. An entry in the chart induces two such partitions, one at the left edge of the entry and one at the right edge.
we obtain two such maximal paths and for any ATG G in this entry and any vertex v not in or adjacent to one of these paths, either v is not in G or v has the same neighbourhood in G as it has in the base ATG.