Forum of Mathematics, Sigma (Jan 2024)

Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes

  • Minki Kim,
  • Alan Lew

DOI
https://doi.org/10.1017/fms.2024.23
Journal volume & issue
Vol. 12

Abstract

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We present extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes, providing a common generalization to the matroidal versions of the theorem due to Kalai and Meshulam, the ‘very colorful’ Helly theorem introduced by Arocha, Bárány, Bracho, Fabila and Montejano and the ‘semi-intersecting’ colorful Helly theorem proved by Montejano and Karasev.

Keywords