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In Search of Hyperpaths

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Abstract

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 \(d=2\).

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Notes

  1. Throughout this paper, unless stated otherwise, given a prime n, all arithmetic equations are mod n, and we often replace the congruence relation \(\equiv \) by an equality sign when no confusion is possible.

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Acknowledgements

We thank Roy Meshulam for insightful comments on this manuscript.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Hebrew University, 91904, Jerusalem, Israel

    Amir Dahari & Nathan Linial

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  1. Amir Dahari
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  2. Nathan Linial
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Correspondence to Amir Dahari.

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

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Dahari, A., Linial, N. In Search of Hyperpaths. Discrete Comput Geom 69, 399–421 (2023). https://doi.org/10.1007/s00454-021-00360-x

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  • DOI: https://doi.org/10.1007/s00454-021-00360-x

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