On Domination Elimination Orderings and Domination Graphs (Extended Abstract)

Several efficient algorithms have been proposed to construct a perfect elimination ordering of the vertices of a chordal graph. We study a generalization of perfect elimination orderings, so called domination elimination orderings (deo). We show that graphs with the property that each induced subgraph has a deo (domination graphs) are related to formulas that can be reduced to formulas with a very simple structure. We also show that every brittle graph and every graph with no induced house and no chordless cycle of length at least five (HC-free graphs) are domination graphs. Moreover, every ordering produced by the Maximum Cardinality Search Procedure on an HC-free graph is a deo.

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