Connected Domination and Steiner Set on Asteroidal Triple-Free Graphs

نویسندگان

  • Hari Balakrishnan
  • Anand Rajaraman
  • C. Pandu Rangan
چکیده

An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighl.)ourhood of the third. Graphs that do not. co~,tain 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-tinm 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. [9] that these two problems are algorithmically closely related.

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تاریخ انتشار 1993