Discrete & Computational Geometry

, Volume 28, Issue 2, pp 223–229

Triangulated Spheres and Colored Cliques

  • Aharoni
  • Chudnovsky
  • Kotlov
Article

DOI: 10.1007/s00454-002-2792-6

Cite this article as:
Aharoni, Chudnovsky & Kotlov Discrete Comput Geom (2002) 28: 223. doi:10.1007/s00454-002-2792-6

Abstract

In [1] a generalization of Hall’s theorem was proved for families of hypergraphs. The proof used Sperner’s lemma. In [5] Meshulam proved an extension of this result, using homology and the nerve theorem. In this paper we show how the triangulations method can be used to derive Meshulam’s results. As in [1], the proof is based on results on extensions of triangulations from the sphere to the full ball. A typical result of this type is that any triangulation of the (d-1) -dimensional sphere Sd-1 can be extended to a triangulation of the ball Bd , by adding one point at a time, having degree at most 2d to its predecessors.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Aharoni
    • 1
  • Chudnovsky
    • 1
  • Kotlov
    • 1
  1. 1.Department of Mathematics, Technion, Haifa 32000, IsraelIsrael