An efficient algorithm for finding a two-pair, and its applications
Discrete Applied Mathematics
Information Processing Letters
Algorithms for weakly triangulated graphs
Discrete Applied Mathematics
Generating weakly triangulated graphs
Journal of Graph Theory
Meyniel weakly triangulated graphs—I: co-perfect orderability
Discrete Applied Mathematics
Meyniel weakly triangulated graphs II: a theorem of Dirac
Discrete Applied Mathematics
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A fast algorithm for building lattices
Information Processing Letters
Weakly chordal graph algorithms via handles
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Treewidth and minimum fill-in of weakly triangulated graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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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 recognition algorithm which, unlike the previous ones, is not based on the notion of 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.