Anagram-free Graph Colouring
An anagram is a word of the form \(WP\) where \(W\) is a non-empty word and \(P\) is a permutation of \(W\). We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. W...
Gespeichert in:
Veröffentlicht in: | arXiv.org 2017-06 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | |
container_title | arXiv.org |
container_volume | |
creator | Wilson, Tim E Wood, David R |
description | An anagram is a word of the form \(WP\) where \(W\) is a non-empty word and \(P\) is a permutation of \(W\). We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and \(k\)-anagram-free colouring. |
format | Article |
fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2076009775</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2076009775</sourcerecordid><originalsourceid>FETCH-proquest_journals_20760097753</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSQccxLTC9KzNVNK0pNVXAvSizIUHDOz8kvLcrMS-dhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWUCFeUCpeCMDczMDA0tzc1Nj4lQBAA5gK2E</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2076009775</pqid></control><display><type>article</type><title>Anagram-free Graph Colouring</title><source>Free E- Journals</source><creator>Wilson, Tim E ; Wood, David R</creator><creatorcontrib>Wilson, Tim E ; Wood, David R</creatorcontrib><description>An anagram is a word of the form \(WP\) where \(W\) is a non-empty word and \(P\) is a permutation of \(W\). We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and \(k\)-anagram-free colouring.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Graph coloring ; Lower bounds ; Permutations</subject><ispartof>arXiv.org, 2017-06</ispartof><rights>2017. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Wilson, Tim E</creatorcontrib><creatorcontrib>Wood, David R</creatorcontrib><title>Anagram-free Graph Colouring</title><title>arXiv.org</title><description>An anagram is a word of the form \(WP\) where \(W\) is a non-empty word and \(P\) is a permutation of \(W\). We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and \(k\)-anagram-free colouring.</description><subject>Graph coloring</subject><subject>Lower bounds</subject><subject>Permutations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSQccxLTC9KzNVNK0pNVXAvSizIUHDOz8kvLcrMS-dhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWUCFeUCpeCMDczMDA0tzc1Nj4lQBAA5gK2E</recordid><startdate>20170627</startdate><enddate>20170627</enddate><creator>Wilson, Tim E</creator><creator>Wood, David R</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20170627</creationdate><title>Anagram-free Graph Colouring</title><author>Wilson, Tim E ; Wood, David R</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20760097753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Graph coloring</topic><topic>Lower bounds</topic><topic>Permutations</topic><toplevel>online_resources</toplevel><creatorcontrib>Wilson, Tim E</creatorcontrib><creatorcontrib>Wood, David R</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wilson, Tim E</au><au>Wood, David R</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Anagram-free Graph Colouring</atitle><jtitle>arXiv.org</jtitle><date>2017-06-27</date><risdate>2017</risdate><eissn>2331-8422</eissn><abstract>An anagram is a word of the form \(WP\) where \(W\) is a non-empty word and \(P\) is a permutation of \(W\). We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al. (2002) asked whether anagram-free chromatic number is bounded by a function of the maximum degree. We answer this question in the negative by constructing graphs with maximum degree 3 and unbounded anagram-free chromatic number. We also prove upper and lower bounds on the anagram-free chromatic number of trees in terms of their radius and pathwidth. Finally, we explore extensions to edge colouring and \(k\)-anagram-free colouring.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | EISSN: 2331-8422 |
ispartof | arXiv.org, 2017-06 |
issn | 2331-8422 |
language | eng |
recordid | cdi_proquest_journals_2076009775 |
source | Free E- Journals |
subjects | Graph coloring Lower bounds Permutations |
title | Anagram-free Graph Colouring |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T11%3A43%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Anagram-free%20Graph%20Colouring&rft.jtitle=arXiv.org&rft.au=Wilson,%20Tim%20E&rft.date=2017-06-27&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2076009775%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2076009775&rft_id=info:pmid/&rfr_iscdi=true |