On the chromatic numbers of low-dimensional spaces

New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.

Saved in:
Bibliographic Details
Published in:Doklady. Mathematics 2017, Vol.95 (1), p.5-6
Main Authors: Cherkashin, D. D., Raigorodskii, A. M.
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Lower bounds
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3
cites cdi_FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3
container_end_page 6
container_issue 1
container_start_page 5
container_title Doklady. Mathematics
container_volume 95
creator Cherkashin, D. D.
Raigorodskii, A. M.
description New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.
doi_str_mv 10.1134/S106456241701001X
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1889816130</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1889816130</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3</originalsourceid><addsrcrecordid>eNp1kEtLxDAUhYMoOI7-AHcF19F782pmKYMvGJiFCu5KmqZOh7apSYv4781QF4K4ugfO-Q6XQ8glwjUiFzfPCEpIxQTmgAD4dkQWKDlSzRU7TjrZ9OCfkrMY9wBCMoAFYds-G3cus7vgOzM2NuunrnQhZr7OWv9Jq6ZzfWx8b9osDsa6eE5OatNGd_Fzl-T1_u5l_Ug324en9e2GWo5qpEIwqCu2YtbVhkuZgxDGVs4gGCW1loCl0yhNCZyrXKPGktc6IRWKShm-JFdz7xD8x-TiWOz9FNIfsUCtVxoVckgpnFM2-BiDq4shNJ0JXwVCcZim-DNNYtjMxJTt31341fwv9A1VrGO3</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1889816130</pqid></control><display><type>article</type><title>On the chromatic numbers of low-dimensional spaces</title><source>Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List</source><creator>Cherkashin, D. D. ; Raigorodskii, A. M.</creator><creatorcontrib>Cherkashin, D. D. ; Raigorodskii, A. M.</creatorcontrib><description>New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S106456241701001X</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Euclidean geometry ; Euclidean space ; Lower bounds ; Mathematics ; Mathematics and Statistics</subject><ispartof>Doklady. Mathematics, 2017, Vol.95 (1), p.5-6</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Copyright Springer Science &amp; Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3</citedby><cites>FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Cherkashin, D. D.</creatorcontrib><creatorcontrib>Raigorodskii, A. M.</creatorcontrib><title>On the chromatic numbers of low-dimensional spaces</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.</description><subject>Euclidean geometry</subject><subject>Euclidean space</subject><subject>Lower bounds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1064-5624</issn><issn>1531-8362</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLxDAUhYMoOI7-AHcF19F782pmKYMvGJiFCu5KmqZOh7apSYv4781QF4K4ugfO-Q6XQ8glwjUiFzfPCEpIxQTmgAD4dkQWKDlSzRU7TjrZ9OCfkrMY9wBCMoAFYds-G3cus7vgOzM2NuunrnQhZr7OWv9Jq6ZzfWx8b9osDsa6eE5OatNGd_Fzl-T1_u5l_Ug324en9e2GWo5qpEIwqCu2YtbVhkuZgxDGVs4gGCW1loCl0yhNCZyrXKPGktc6IRWKShm-JFdz7xD8x-TiWOz9FNIfsUCtVxoVckgpnFM2-BiDq4shNJ0JXwVCcZim-DNNYtjMxJTt31341fwv9A1VrGO3</recordid><startdate>2017</startdate><enddate>2017</enddate><creator>Cherkashin, D. D.</creator><creator>Raigorodskii, A. M.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2017</creationdate><title>On the chromatic numbers of low-dimensional spaces</title><author>Cherkashin, D. D. ; Raigorodskii, A. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Euclidean geometry</topic><topic>Euclidean space</topic><topic>Lower bounds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cherkashin, D. D.</creatorcontrib><creatorcontrib>Raigorodskii, A. M.</creatorcontrib><collection>CrossRef</collection><jtitle>Doklady. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cherkashin, D. D.</au><au>Raigorodskii, A. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the chromatic numbers of low-dimensional spaces</atitle><jtitle>Doklady. Mathematics</jtitle><stitle>Dokl. Math</stitle><date>2017</date><risdate>2017</risdate><volume>95</volume><issue>1</issue><spage>5</spage><epage>6</epage><pages>5-6</pages><issn>1064-5624</issn><eissn>1531-8362</eissn><abstract>New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S106456241701001X</doi><tpages>2</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1064-5624
ispartof Doklady. Mathematics, 2017, Vol.95 (1), p.5-6
issn 1064-5624
1531-8362
language eng
recordid cdi_proquest_journals_1889816130
source Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List
subjects Euclidean geometry
Euclidean space
Lower bounds
Mathematics
Mathematics and Statistics
title On the chromatic numbers of low-dimensional spaces
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-23T23%3A08%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20chromatic%20numbers%20of%20low-dimensional%20spaces&rft.jtitle=Doklady.%20Mathematics&rft.au=Cherkashin,%20D.%20D.&rft.date=2017&rft.volume=95&rft.issue=1&rft.spage=5&rft.epage=6&rft.pages=5-6&rft.issn=1064-5624&rft.eissn=1531-8362&rft_id=info:doi/10.1134/S106456241701001X&rft_dat=%3Cproquest_cross%3E1889816130%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c316t-4420fd292cefa3557044acdea10a6588501be815ab033678181b3f8fd2d14d6a3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1889816130&rft_id=info:pmid/&rfr_iscdi=true