Large simple d-cycles in simplicial complexes

Roy Meshulam; Ilan Newman; Yuri Rabinovich

doi:10.1007/s11856-023-2512-x

Large simple d-cycles in simplicial complexes

Roy Meshulam, Ilan Newman, Yuri Rabinovich

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the size of the largest simple d-cycle in a simplicial d-complex K is at least a square root of K’s density. This is a higher dimensional relative of a classical result of Erdős and Gallai [7], claiming that any graph G contains a simple cycle of size at least linear in G’s density.

Original language	English
Pages (from-to)	581-597
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	256
Issue number	2
DOIs	https://doi.org/10.1007/s11856-023-2512-x
State	Published - Sep 2023

Bibliographical note

Funding Information:
Supported in part by the Israel Science Foundation, grant 326/16.

Funding Information:
We are very grateful to Jan van den Heuvel from the London School of Economics for an insightful discussion which led to the formulation of the main question addressed in this paper.

Funding Information:
Supported in part by the Israel Science Foundation, grant 497/17. Acknowledgements

Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s11856-023-2512-x

Cite this

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Large simple d-cycles in simplicial complexes

Abstract

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