1996-01-01
Characterizing Proximity Trees
Publication
Publication
Algorithmica
,
Volume 16
-
Issue 1
p. 83-
110
Complete characterizations are given for those trees that can be drawn as either the relative neighborhood graph, relatively closest graph, Gabriel graph, or modified Gabriel graph of a set of points in the plane. The characterizations give rise to linear-time algorithms for determining whether a tree has such a drawing; if such a drawing exists one can be constructed in linear time in the real RAM model. The characterization of Gabriel graphs settles several conjectures of Matula and Sokal [17].
| Additional Metadata | |
|---|---|
| Keywords | Delaunay triangulation, Gabriel graph, Graph drawing, Minimum spanning tree, Proximity graphs, Relative neighborhood graph, Relatively closest graph, Trees |
| Persistent URL | dx.doi.org/10.1007/BF02086609 |
| Journal | Algorithmica |
| Citation |
Bose, P, Lenhart, W. (W.), & Liotta, G. (G.). (1996). Characterizing Proximity Trees. Algorithmica, 16(1), 83–110. doi:10.1007/BF02086609
|