On the existence of total dominating subgraphs with a prescribed additive hereditary property
نویسنده
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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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 311 شماره
صفحات -
تاریخ انتشار 2011