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

Technion - Israel Institute of Technology, University of Haifa

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-023-2512-x

Cite this

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title = "Large simple d-cycles in simplicial complexes",

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{\textquoteright}s density. This is a higher dimensional relative of a classical result of Erd{\H o}s and Gallai [7], claiming that any graph G contains a simple cycle of size at least linear in G{\textquoteright}s density.",

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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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DO - 10.1007/s11856-023-2512-x

M3 - مقالة

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VL - 256

SP - 581

EP - 597

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

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Large simple d-cycles in simplicial complexes

Abstract

All Science Journal Classification (ASJC) codes

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