Circuit Admissible Triangulations of Oriented Matroids
Please always quote using this URN: urn:nbn:de:0297-zib-6139
- All triangulations of euclidean oriented matroids are of the same PL-homeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PL-spheres. For non-euclidean oriented matroids this question is wide open. One key point in the proof of Anderson is the following fact: for every triangulation of a euclidean oriented matroid the adjacency graph of the set of all simplices ``intersecting'' a segment $[p_-p_+]$ is a path. We call this graph the $[p_-p_+]$-adjacency graph of the triangulation. While we cannot solve the problem of the topological type of triangulations of general oriented matroids we show in this note that for every circuit admissible triangulation of an arbitrary oriented matroid the $[p_-p_+]$-adjacency graph is a path.
Author: | Jörg Rambau |
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Document Type: | ZIB-Report |
Tag: | segment adjacency graph; topological type; triangulations of oriented matroids |
MSC-Classification: | 52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C40 Oriented matroids |
Date of first Publication: | 2000/12/11 |
Series (Serial Number): | ZIB-Report (00-45) |
ZIB-Reportnumber: | 00-45 |
Published in: | Appeared in: Discrete u. Computational Geometry, Vol. 27, No. 1 (2002) 155-161 |