Connected domination and steiner set on asteroidal triple-free graphs
An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighbourhood of the third. Graphs that do not contain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect. We present efficient polynomial-time algorithms for the minimum cardinality connected dominating set problem and the Steiner set problem on AT-free graphs. These results, in addition to solving these problems on this large class of graphs, also strengthen the conjecture of White. et. al.  that these two problems are algorithmically closely related.
KeywordsDesign of algorithms asteroidal-triple free graphs
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- D.G. Corneil, S. Olariu, and L. Stewart. Asteroidal triple-free graphs. Technical Report 262/92, University of Toronto, June 1992.Google Scholar
- M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Fransisco, CA, 1979.Google Scholar
- M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, 1980.Google Scholar
- C.G. Lekkerkerker and J.C. Boland. Representation of a finite graph by a set of intervals on a real line. Fundamenta Mathematicae, 51:45–64, 1962.Google Scholar
- K. White, M. Farber, and W.R. Pulleybank. Steiner trees, connected domination and strongly chordal graphs. Networks, 15:109–124, 1985.Google Scholar