In Search of Hyperpaths

Amir Dahari*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study hyperpaths—a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A d-dimensional hyperpath is a d-dimensional hypertree in which every (d- 1) -dimensional face is contained in at most (d+ 1) faces of dimension d. We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension d= 2.

Original languageEnglish
Pages (from-to)399-421
Number of pages23
JournalDiscrete and Computational Geometry
Issue number2
Early online date7 Jan 2022
StateE-pub ahead of print - 7 Jan 2022

Bibliographical note

Funding Information:
Supported by BSF US-Israel Grant 2018313 “Between topology and combinatorics”

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Finite fields
  • High dimensional combinatorics
  • Hypertrees
  • Linear algebra
  • Matrix multiplication
  • Simplicial complexes


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