## Abstract Suppose __G = (V, E)__ is a graph in which every vertex __x__ has a nonβnegative real number __w(x)__ as its weight. The __w__βdistance sum of a vertex __y__ is __D~G, w~(y)__ = Ο~xβ v~ __d(y, x)w(x).__ The __w__βmedian of __G__ is the set of all vertices __y__ with minimum __w__βdistanc
Local medians in chordal graphs
β Scribed by Heiko Wittenberg
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 535 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
A chordal graph has a dominating clique iff it has diameter at most 3. A strongly chordal graph which has a dominating clique has one as small as the smallest dominating set-and, furthermore, there is a linear-time algorithm to find such a small dominating clique.
Chordal graphs are graphs with the property that each cycle of length greater than 3 has two non-consecutive vertices that are joined by an edge. An important subclass of chordal graphs are strongly chordal graphs (Farber, 1983). Chordal graphs appear for example in the design of acyclic data base s
The main result of this paper is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs. This is proved by a sophisticated reduction from SATISFIABILITY. As a corollary, HAMILTONIAN CIRCUIT is NP-complete for strongly chordal split graphs. On both classes the complexity