Abstract
A recent result by Pach and Pinchasi on so-called balanced lines of a finite two-colored point set in the plane is related to other facts on halving triangles in 3-space and to a special case of the Generalized Lower Bound Theorem for convexpo lytopes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artur Andrzejak and Emo Welzl, In between k-sets, j-facets, and i-faces: (i, j)-partitions, Discrete Comput. Geom. 29 (2003), 105–131.
Artur Andrzejak, Boris Aronov, Sariel Har-Peled, Raimund Seidel, and Emo Welzl, Results on k-sets and j-facets via continuous motion, in“Proc 14th Ann. ACM Symp. on Comput.Geom.” (1998), 192–199.
Paul Erdos, Laszlo Lovasz, A. Simmons, and Ernst G. Straus, Dissection graphs of planar point sets, in A Survey of Combinatorial Theory (J.N. Srivastava et al., Eds.), North Holland (1973), 139–149.
Carl W. Lee, Winding numbers and the generalized lower-bound conjecture, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 6 (1991), 209–219.
Laszlo Lovasz, On the number of halving lines, Ann. Universitatis Scientarium Budapest, E¨otv¨os, Sectio Mathematica 14 (1971), 107–108.
Peter McMullen, On simple polytopes, Inventiones Math. 113 (1993), 419–444.
Janos Pach and Rom Pinchasi, On the number of balanced lines, Discrete Comput. Geom. 25 (2001), 611–628.
Richard P. Stanley, The number of faces of simplicial polytopes and spheres, in “Discrete Geometry and Convexity”, (J. E. Goodman, E. Lutwak, J. Malkevitch, and R. Pollack, Eds.), Annals NewY ork Academy of Sciences 440 (1985), 212–223.
Emo Welzl, Entering and leaving j-facets, Discrete Comput. Geom. 25 (2001), 351–364.
Gunter M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics, Springer-Verlag (1995).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sharir, M., Welzl, E. (2003). Balanced Lines, Halving Triangles, and the Generalized Lower Bound Theorem. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-55566-4_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62442-1
Online ISBN: 978-3-642-55566-4
eBook Packages: Springer Book Archive