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.
Work supported in part by the National Science Foundation under grant CCR-8909996
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© 1995 Springer-Verlag Berlin Heidelberg
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Dahihaus, E., Hammer, P., Maffray, F., Olariu, S. (1995). On domination elimination orderings and domination graphs. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_39
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DOI: https://doi.org/10.1007/3-540-59071-4_39
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