to some vertex in . The minimal -separators also form an algebraic structure: For two fixed vertices and of a given graph , an -separator can be regarded as a predecessor of another -separator , if every path from to meets before it meets . More rigorously, the predecessor relation is defined as follows: Let and be two -separators in . Then is a predecessor of , in symbols , if for each , every path connecting to meets . It follows from the definition that the predecessor relation yields a preorder on the set of all -separators. Furthermore, proved that the predecessor relation gives rise to a complete lattice when restricted to the set of minimal -separators in . See also Chordal graph, a graph in which every minimal separator is a clique. k-vertex-connected graph Notes References . . Graph connectivity