The tree-free domination number y(G; -Fk), k ≥ 2, of a graph G is the minimum cardinality of a dominating set S in G such that the subgraph (S) induced by S contains no tree on k vertices as a (not necessarily induced) subgraph (equivalently, each component of (S) has cardinality less than k). When k = 2, the tree-free domination number is the independent domination number. We obtain a characterization of trees with equal domination and tree-free domination numbers. This generalizes a result of Cockayne et al. (A characterisation of (y,i)-trees. J. Graph Theory 34(4) (2000) 277-292).
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-20172 |
| Date | 01 June 2002 |
| Creators | Haynes, Teresa W., Henning, Michael A. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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