Rainbows in the Hypercube
Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest n...
Gespeichert in:
| Veröffentlicht in: | Graphs and combinatorics 2007-04, Vol.23 (2), p.123-133 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 133 |
|---|---|
| container_issue | 2 |
| container_start_page | 123 |
| container_title | Graphs and combinatorics |
| container_volume | 23 |
| creator | Axenovich, Maria Harborth, Heiko Kemnitz, Arnfried Möller, Meinhard Schiermeyer, Ingo |
| description | Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest number of colors such that there exists an edge coloring of G with f(G,H) colors such that no subgraph isomorphic to H is rainbow. In this paper we start the investigation of this anti-Ramsey problem by providing bounds on f(Qn,Qk) which are asymptotically tight for k = 2 and by giving some exact results. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/s00373-007-0691-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_207359230</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1257758061</sourcerecordid><originalsourceid>FETCH-LOGICAL-c272t-cfff8b8e1d9577e63e9be85348af21c1d486dfd7d180aedaa3bebb504a8ccd233</originalsourceid><addsrcrecordid>eNotkE1LxDAURYMoWEd_wOyK--h7TdMkSxnUEQYE0XXIJ3bQtiYtMv_elrq6Z3G5Fw4hW4Q7BBD3GYAJRmek0CikzRkpsGaccoX1OSlAIVJAVJfkKucjAHCsoSDbN9N2tv_NZduV42co96chJDfZcE0uovnK4eY_N-Tj6fF9t6eH1-eX3cOBukpUI3UxRmllQK-4EKFhQdkgOauliRU69LVsfPTCowQTvDHMBms51EY65yvGNuR23R1S_zOFPOpjP6VuvtQVCMZVxWAu4Vpyqc85haiH1H6bdNIIehGgVwF6wUWAbtgf4E1NCg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>207359230</pqid></control><display><type>article</type><title>Rainbows in the Hypercube</title><source>SpringerLink</source><creator>Axenovich, Maria ; Harborth, Heiko ; Kemnitz, Arnfried ; Möller, Meinhard ; Schiermeyer, Ingo</creator><creatorcontrib>Axenovich, Maria ; Harborth, Heiko ; Kemnitz, Arnfried ; Möller, Meinhard ; Schiermeyer, Ingo</creatorcontrib><description>Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest number of colors such that there exists an edge coloring of G with f(G,H) colors such that no subgraph isomorphic to H is rainbow. In this paper we start the investigation of this anti-Ramsey problem by providing bounds on f(Qn,Qk) which are asymptotically tight for k = 2 and by giving some exact results. [PUBLICATION ABSTRACT]</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-007-0691-6</identifier><language>eng</language><publisher>Tokyo: Springer Nature B.V</publisher><subject>Asymptotic methods ; Color ; Computer science ; Graphs ; Mathematics</subject><ispartof>Graphs and combinatorics, 2007-04, Vol.23 (2), p.123-133</ispartof><rights>Springer-Verlag Tokyo 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c272t-cfff8b8e1d9577e63e9be85348af21c1d486dfd7d180aedaa3bebb504a8ccd233</citedby><cites>FETCH-LOGICAL-c272t-cfff8b8e1d9577e63e9be85348af21c1d486dfd7d180aedaa3bebb504a8ccd233</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>Axenovich, Maria</creatorcontrib><creatorcontrib>Harborth, Heiko</creatorcontrib><creatorcontrib>Kemnitz, Arnfried</creatorcontrib><creatorcontrib>Möller, Meinhard</creatorcontrib><creatorcontrib>Schiermeyer, Ingo</creatorcontrib><title>Rainbows in the Hypercube</title><title>Graphs and combinatorics</title><description>Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest number of colors such that there exists an edge coloring of G with f(G,H) colors such that no subgraph isomorphic to H is rainbow. In this paper we start the investigation of this anti-Ramsey problem by providing bounds on f(Qn,Qk) which are asymptotically tight for k = 2 and by giving some exact results. [PUBLICATION ABSTRACT]</description><subject>Asymptotic methods</subject><subject>Color</subject><subject>Computer science</subject><subject>Graphs</subject><subject>Mathematics</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNotkE1LxDAURYMoWEd_wOyK--h7TdMkSxnUEQYE0XXIJ3bQtiYtMv_elrq6Z3G5Fw4hW4Q7BBD3GYAJRmek0CikzRkpsGaccoX1OSlAIVJAVJfkKucjAHCsoSDbN9N2tv_NZduV42co96chJDfZcE0uovnK4eY_N-Tj6fF9t6eH1-eX3cOBukpUI3UxRmllQK-4EKFhQdkgOauliRU69LVsfPTCowQTvDHMBms51EY65yvGNuR23R1S_zOFPOpjP6VuvtQVCMZVxWAu4Vpyqc85haiH1H6bdNIIehGgVwF6wUWAbtgf4E1NCg</recordid><startdate>200704</startdate><enddate>200704</enddate><creator>Axenovich, Maria</creator><creator>Harborth, Heiko</creator><creator>Kemnitz, Arnfried</creator><creator>Möller, Meinhard</creator><creator>Schiermeyer, Ingo</creator><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>200704</creationdate><title>Rainbows in the Hypercube</title><author>Axenovich, Maria ; Harborth, Heiko ; Kemnitz, Arnfried ; Möller, Meinhard ; Schiermeyer, Ingo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c272t-cfff8b8e1d9577e63e9be85348af21c1d486dfd7d180aedaa3bebb504a8ccd233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Asymptotic methods</topic><topic>Color</topic><topic>Computer science</topic><topic>Graphs</topic><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Axenovich, Maria</creatorcontrib><creatorcontrib>Harborth, Heiko</creatorcontrib><creatorcontrib>Kemnitz, Arnfried</creatorcontrib><creatorcontrib>Möller, Meinhard</creatorcontrib><creatorcontrib>Schiermeyer, Ingo</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Axenovich, Maria</au><au>Harborth, Heiko</au><au>Kemnitz, Arnfried</au><au>Möller, Meinhard</au><au>Schiermeyer, Ingo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Rainbows in the Hypercube</atitle><jtitle>Graphs and combinatorics</jtitle><date>2007-04</date><risdate>2007</risdate><volume>23</volume><issue>2</issue><spage>123</spage><epage>133</epage><pages>123-133</pages><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest number of colors such that there exists an edge coloring of G with f(G,H) colors such that no subgraph isomorphic to H is rainbow. In this paper we start the investigation of this anti-Ramsey problem by providing bounds on f(Qn,Qk) which are asymptotically tight for k = 2 and by giving some exact results. [PUBLICATION ABSTRACT]</abstract><cop>Tokyo</cop><pub>Springer Nature B.V</pub><doi>10.1007/s00373-007-0691-6</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0911-0119 |
| ispartof | Graphs and combinatorics, 2007-04, Vol.23 (2), p.123-133 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_journals_207359230 |
| source | SpringerLink |
| subjects | Asymptotic methods Color Computer science Graphs Mathematics |
| title | Rainbows in the Hypercube |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-07T17%3A21%3A55IST&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=Rainbows%20in%20the%20Hypercube&rft.jtitle=Graphs%20and%20combinatorics&rft.au=Axenovich,%20Maria&rft.date=2007-04&rft.volume=23&rft.issue=2&rft.spage=123&rft.epage=133&rft.pages=123-133&rft.issn=0911-0119&rft.eissn=1435-5914&rft_id=info:doi/10.1007/s00373-007-0691-6&rft_dat=%3Cproquest_cross%3E1257758061%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=207359230&rft_id=info:pmid/&rfr_iscdi=true |