Slicing all Edges of an n-cube Requires n2/3 Hyperplanes

Ohad Klein

doi:10.1109/focs57990.2023.00117

Slicing all Edges of an n-cube Requires n^2/3 Hyperplanes

Ohad Klein

Hebrew University of Jerusalem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Consider the n-cube graph with vertices {-1,1}n and edges connecting vertices with Hamming distance 1. How many hyperplanes in Rn are needed in order to dissect all edges? We show that at least Ω(n2/3) are needed, which improves the previous bound of Ω(n0.51) by Yehuda and Yehudayoff.

Original language	English
Title of host publication	Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023
Publisher	IEEE Computer Society
Pages	1931-1936
Number of pages	6
ISBN (Electronic)	9798350318944
DOIs	https://doi.org/10.1109/focs57990.2023.00117
State	Published - 2023
Externally published	Yes
Event	64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 - Santa Cruz, United States Duration: 6 Nov 2023 → 9 Nov 2023

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)	0272-5428

Conference

Conference	64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023
Country/Territory	United States
City	Santa Cruz
Period	6/11/23 → 9/11/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Access to Document

10.1109/focs57990.2023.00117

Cite this

@inproceedings{16c52eaf69974e56b475dccc1ad7115e,

title = "Slicing all Edges of an n-cube Requires n2/3 Hyperplanes",

abstract = "Consider the n-cube graph with vertices {-1,1}n and edges connecting vertices with Hamming distance 1. How many hyperplanes in Rn are needed in order to dissect all edges? We show that at least Ω(n2/3) are needed, which improves the previous bound of Ω(n0.51) by Yehuda and Yehudayoff.",

author = "Ohad Klein",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 ; Conference date: 06-11-2023 Through 09-11-2023",

year = "2023",

doi = "10.1109/focs57990.2023.00117",

language = "אנגלית",

series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

publisher = "IEEE Computer Society",

pages = "1931--1936",

booktitle = "Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023",

address = "ארצות הברית",

}

Klein, O 2023, Slicing all Edges of an n-cube Requires n^2/3 Hyperplanes. in Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, IEEE Computer Society, pp. 1931-1936, 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023, Santa Cruz, United States, 6/11/23. https://doi.org/10.1109/focs57990.2023.00117

Slicing all Edges of an n-cube Requires n^2/3 Hyperplanes. / Klein, Ohad.
Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023. IEEE Computer Society, 2023. p. 1931-1936 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Slicing all Edges of an n-cube Requires n2/3 Hyperplanes

AU - Klein, Ohad

PY - 2023

Y1 - 2023

N2 - Consider the n-cube graph with vertices {-1,1}n and edges connecting vertices with Hamming distance 1. How many hyperplanes in Rn are needed in order to dissect all edges? We show that at least Ω(n2/3) are needed, which improves the previous bound of Ω(n0.51) by Yehuda and Yehudayoff.

AB - Consider the n-cube graph with vertices {-1,1}n and edges connecting vertices with Hamming distance 1. How many hyperplanes in Rn are needed in order to dissect all edges? We show that at least Ω(n2/3) are needed, which improves the previous bound of Ω(n0.51) by Yehuda and Yehudayoff.

UR - http://www.scopus.com/inward/record.url?scp=85182404522&partnerID=8YFLogxK

U2 - 10.1109/focs57990.2023.00117

DO - 10.1109/focs57990.2023.00117

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85182404522

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 1931

EP - 1936

BT - Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023

PB - IEEE Computer Society

T2 - 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023

Y2 - 6 November 2023 through 9 November 2023

ER -