Recognizing Weakly Triangulated Graphs by Edge Separability

We apply Lekkerkerker and Boland's recognition algorithm for triangulated graphs to the class of weakly triangulated graphs. This yields a new characterization of weakly triangulated graphs, as well as a new O(m2) recognition algorithm which, unlike the previous ones, is not based on the notion of a 2-pair, but rather on the structural properties of the minimal separators of the graph. It also gives the strongest relationship to the class of triangulated graphs that has been established so far.

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