Counting facets and incidences

Journal Article (Journal Article)

We show that m distinct cells in an arrangement of n planes in ℝ3 are bounded by O(m2/3n+n2) faces, which in turn yields a tight bound on the maximum number of facets bounding m cells in an arrangement of n hyperplanes in ℝd, for every d≥3. In addition, the method is extended to obtain tight bounds on the maximum number of faces on the boundary of all nonconvex cells in an arrangement of triangles in ℝ3. We also present a simpler proof of the O(m2/3nd/3+nd-1) bound on the number of incidences between n hyperplanes in ℝd and m vertices of their arrangement. © 1992 Springer-Verlag New York Inc.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Aronov, B

Published Date

  • December 1, 1992

Published In

Volume / Issue

  • 7 / 1

Start / End Page

  • 359 - 369

Electronic International Standard Serial Number (EISSN)

  • 1432-0444

International Standard Serial Number (ISSN)

  • 0179-5376

Digital Object Identifier (DOI)

  • 10.1007/BF02187848

Citation Source

  • Scopus