Separability generalizes Dirac's theorem
Discrete Applied Mathematics
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs
SIAM Journal on Computing
A practical algorithm for making filled graphs minimal
Theoretical Computer Science
On Domination Elimination Orderings and Domination Graphs (Extended Abstract)
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Distributed computing of efficient routing schemes in generalized chordal graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Distributed computing of efficient routing schemes in generalized chordal graphs
Theoretical Computer Science
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Many graph search algorithms use a labelling of the vertices to compute an ordering of the vertices. We examine such algorithms which compute a peo (perfect elimination ordering) of a chordal graph, and corresponding algorithms which compute an meo (minimal elimination ordering) of a non-chordal graph. We express all known peo-computing search algorithms as instances of a generic algorithm called MLS (Maximal Label Search) and generalize Algorithm MLS into CompMLS, which can compute any peo. We then extend these algorithms to versions which compute an meo, and likewise generalize all known meo-computing search algorithms. We show the surprising result that all these search algorithms compute the same set of minimal triangulations, even though the computed meos are different.