Steiner set and connected domination in trapezoid graphs
β Scribed by Y.Daniel Liang
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 710 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Efficient algorithms are developed for finding a minimum cardinality connected dominating set and a minimum cardinality Steiner tree in permutation graphs. This contrasts with the known NP-completeness of both problems on comparability graphs in general.
## Abstract Let __G__ = (__V, E__) be a connected graph. A set __D__ β __V__ is a __setβdominating set__ (sdβset) if for every set __T__ β __V__ β __D__, there exists a nonempty set __S__ β __D__ such that the subgraph γ__S__ βͺ __T__γ induced by __S__ βͺ __T__ is connected. The setβdomination number
Suppose G is a graph on n vertices with minimum degree r. Using standard random methods it is shown that there exists a two-coloring of the vertices of G with colors, +1 and &1, such that all closed neighborhoods contain more 1's than &1's, and all together the number of 1's does not exceed the numb