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

Ohad Klein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationProceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023
PublisherIEEE Computer Society
Pages1931-1936
Number of pages6
ISBN (Electronic)9798350318944
DOIs
StatePublished - 2023
Externally publishedYes
Event64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 - Santa Cruz, United States
Duration: 6 Nov 20239 Nov 2023

Publication series

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

Conference

Conference64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023
Country/TerritoryUnited States
CitySanta Cruz
Period6/11/239/11/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Fingerprint

Dive into the research topics of 'Slicing all Edges of an n-cube Requires n2/3 Hyperplanes'. Together they form a unique fingerprint.

Cite this