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

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-023-2512-x

Cite this

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AB - 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.

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Large simple d-cycles in simplicial complexes

Abstract

Bibliographical note

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