Triangulated spheres and colored cliques

Ron Aharoni, Maria Chudnovsky, Andrei Kotlov

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)223-229
Number of pages7
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Sep 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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