On the existence of total dominating subgraphs with a prescribed additive hereditary property

نویسنده

  • Oliver Schaudt
چکیده

Recently, Bacsó and Tuza gave a full characterization of the graphs for which every connected induced subgraph has a connected dominating subgraph satisfying an arbitrary prescribed hereditary property. Using their result, we derive a similar characterization of the graphs for which any isolate-free induced subgraph has a total dominating subgraph that satisfies a prescribed additive hereditary property. In particular, we give a characterization for the case where the total dominating subgraphs are disjoint union of complete graphs. This yields a characterization of the graphs for which every isolate-free induced subgraph has a vertex-dominating induced matching, a so-called induced paired-dominating set.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 311  شماره 

صفحات  -

تاریخ انتشار 2011