List Ramsey numbers
We introduce the list colouring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are far apart. For $\ell$-uniform cliques we prove th...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Alon, N Bucić, M Kalvari, T Kuperwasser, E Szabó, T |
| description | We introduce the list colouring extension of classical Ramsey numbers. We
investigate when the two Ramsey numbers are equal, and in general, how far
apart they can be from each other. We find graph sequences where the two are
equal and where they are far apart. For $\ell$-uniform cliques we prove that
the list Ramsey number is bounded by an exponential function, while it is
well-known that the Ramsey number is super-exponential for uniformity at least
$3$. This is in great contrast to the graph case where we cannot even decide
the question of equality for cliques. |
| doi_str_mv | 10.48550/arxiv.1902.07018 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1902_07018</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1902_07018</sourcerecordid><originalsourceid>FETCH-LOGICAL-a678-fd5fbeb847a018b54da2d9e82d3f67a0c9976d1da38a9467bfcc3ec0db49119b3</originalsourceid><addsrcrecordid>eNotzjsLwjAYheEsDlKdnJzsH2hNmvsoxRsUBOlevjQJFKxIomL_vfUyHTjDy4PQkuCcKc7xGsKre-ZE4yLHEhM1RYuqi_f0DH10Q3p99MaFOEMTD5fo5v9NUL3b1uUhq077Y7mpMhBSZd5yb5xRTMJYMpxZKKx2qrDUi_FrtZbCEgtUgWZCGt-21LXYGqYJ0YYmaPXLflXNLXQ9hKH56Jqvjr4BbdEz3A</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>List Ramsey numbers</title><source>arXiv.org</source><creator>Alon, N ; Bucić, M ; Kalvari, T ; Kuperwasser, E ; Szabó, T</creator><creatorcontrib>Alon, N ; Bucić, M ; Kalvari, T ; Kuperwasser, E ; Szabó, T</creatorcontrib><description>We introduce the list colouring extension of classical Ramsey numbers. We
investigate when the two Ramsey numbers are equal, and in general, how far
apart they can be from each other. We find graph sequences where the two are
equal and where they are far apart. For $\ell$-uniform cliques we prove that
the list Ramsey number is bounded by an exponential function, while it is
well-known that the Ramsey number is super-exponential for uniformity at least
$3$. This is in great contrast to the graph case where we cannot even decide
the question of equality for cliques.</description><identifier>DOI: 10.48550/arxiv.1902.07018</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2019-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1902.07018$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1902.07018$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Alon, N</creatorcontrib><creatorcontrib>Bucić, M</creatorcontrib><creatorcontrib>Kalvari, T</creatorcontrib><creatorcontrib>Kuperwasser, E</creatorcontrib><creatorcontrib>Szabó, T</creatorcontrib><title>List Ramsey numbers</title><description>We introduce the list colouring extension of classical Ramsey numbers. We
investigate when the two Ramsey numbers are equal, and in general, how far
apart they can be from each other. We find graph sequences where the two are
equal and where they are far apart. For $\ell$-uniform cliques we prove that
the list Ramsey number is bounded by an exponential function, while it is
well-known that the Ramsey number is super-exponential for uniformity at least
$3$. This is in great contrast to the graph case where we cannot even decide
the question of equality for cliques.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjsLwjAYheEsDlKdnJzsH2hNmvsoxRsUBOlevjQJFKxIomL_vfUyHTjDy4PQkuCcKc7xGsKre-ZE4yLHEhM1RYuqi_f0DH10Q3p99MaFOEMTD5fo5v9NUL3b1uUhq077Y7mpMhBSZd5yb5xRTMJYMpxZKKx2qrDUi_FrtZbCEgtUgWZCGt-21LXYGqYJ0YYmaPXLflXNLXQ9hKH56Jqvjr4BbdEz3A</recordid><startdate>20190219</startdate><enddate>20190219</enddate><creator>Alon, N</creator><creator>Bucić, M</creator><creator>Kalvari, T</creator><creator>Kuperwasser, E</creator><creator>Szabó, T</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190219</creationdate><title>List Ramsey numbers</title><author>Alon, N ; Bucić, M ; Kalvari, T ; Kuperwasser, E ; Szabó, T</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-fd5fbeb847a018b54da2d9e82d3f67a0c9976d1da38a9467bfcc3ec0db49119b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Alon, N</creatorcontrib><creatorcontrib>Bucić, M</creatorcontrib><creatorcontrib>Kalvari, T</creatorcontrib><creatorcontrib>Kuperwasser, E</creatorcontrib><creatorcontrib>Szabó, T</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Alon, N</au><au>Bucić, M</au><au>Kalvari, T</au><au>Kuperwasser, E</au><au>Szabó, T</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>List Ramsey numbers</atitle><date>2019-02-19</date><risdate>2019</risdate><abstract>We introduce the list colouring extension of classical Ramsey numbers. We
investigate when the two Ramsey numbers are equal, and in general, how far
apart they can be from each other. We find graph sequences where the two are
equal and where they are far apart. For $\ell$-uniform cliques we prove that
the list Ramsey number is bounded by an exponential function, while it is
well-known that the Ramsey number is super-exponential for uniformity at least
$3$. This is in great contrast to the graph case where we cannot even decide
the question of equality for cliques.</abstract><doi>10.48550/arxiv.1902.07018</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1902.07018 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1902_07018 |
| source | arXiv.org |
| subjects | Mathematics - Combinatorics |
| title | List Ramsey numbers |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T05%3A24%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=List%20Ramsey%20numbers&rft.au=Alon,%20N&rft.date=2019-02-19&rft_id=info:doi/10.48550/arxiv.1902.07018&rft_dat=%3Carxiv_GOX%3E1902_07018%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |