Ample simplicial complexes

Chaim Even-Zohar, Michael Farber, Lewis Mead

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by potential applications in network theory, engineering and computer science, we study r-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property of indestructibility, in the sense that removing any finite number of its simplexes leaves a complex isomorphic to itself. We prove that an r-ample simplicial complex is simply connected and 2-connected for r large. The number n of vertexes of an r-ample simplicial complex satisfies exp(Ω(2rr)). We use the probabilistic method to establish the existence of r-ample simplicial complexes with n vertexes for any n>r2r22r. Finally, we introduce the iterated Paley simplicial complexes, which are explicitly constructed r-ample simplicial complexes with nearly optimal number of vertexes.

Original languageEnglish
JournalEuropean Journal of Mathematics
Volume8
Issue number1
DOIs
StatePublished - Mar 2022
Externally publishedYes

Keywords

  • Ample simplicial complex
  • Iterated Payley complex
  • Rado simplicial complex
  • Random simplicial complex

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