On the existence of total dominating subgraphs with a prescribed additive hereditary property
On the existence of total dominating subgraphs with a prescribed additive hereditary property.
Published in: Discrete Mathematics Vol. 311 (18-19). pp. 2095-2101.
Recently, Bacsô 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.
|Citations:||1 (Google Scholar) | 0 (Web of Science)|
|Uncontrolled Keywords:||total domination structural domination|
|Divisions:||Institute of Computer Science > Computer Science Department - Prof. Dr. Schrader
Mathematical Institute > Prof. Dr. Faigle
|Depositing User:||Oliver Schaudt|
|Date Deposited:||12 Jul 2011 00:00|
|Last Modified:||19 Dec 2011 09:44|