On stabbing triangles by lines in 3-space
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 1, page 109-113
- ISSN: 0010-2628
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topAronov, Boris, and Matoušek, Jiří. "On stabbing triangles by lines in 3-space." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 109-113. <http://eudml.org/doc/247745>.
@article{Aronov1995,
abstract = {We give an example of a set $P$ of $3n$ points in $\mathbb \{R\} 3$ such that, for any partition of $P$ into triples, there exists a line stabbing $\Omega (\sqrt\{n\})$ of the triangles determined by the triples.},
author = {Aronov, Boris, Matoušek, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {combinatorial geometry; computational geometry; crossing number; partition; stabbing},
language = {eng},
number = {1},
pages = {109-113},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On stabbing triangles by lines in 3-space},
url = {http://eudml.org/doc/247745},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Aronov, Boris
AU - Matoušek, Jiří
TI - On stabbing triangles by lines in 3-space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 109
EP - 113
AB - We give an example of a set $P$ of $3n$ points in $\mathbb {R} 3$ such that, for any partition of $P$ into triples, there exists a line stabbing $\Omega (\sqrt{n})$ of the triangles determined by the triples.
LA - eng
KW - combinatorial geometry; computational geometry; crossing number; partition; stabbing
UR - http://eudml.org/doc/247745
ER -
References
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- Pach J., Geometric graphs, In J.E. Goodman, R. Pollack, and W. Steiger, editors, Computational Geometry: Papers from the DIMACS special year; Amer. Math. Soc., 1991. Zbl1052.05004
- Matoušek J., Efficient partition trees, Discrete Comput. Geom. 8 (1992), 315-334. (1992) MR1174360
- Welzl E., private communication, 1992, .
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