A categorification for the signed chromatic polynomial

A categorification for the signed chromatic polynomial

By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups s...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Cheng, Zhiyun, Lei, Ziyi, Wang, Yitian, Zhang, Yanguo
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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 Cheng, Zhiyun
Lei, Ziyi
Wang, Yitian
Zhang, Yanguo
description By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which corresponds to signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.
doi_str_mv 10.48550/arxiv.2101.01661
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2101_01661</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2101_01661</sourcerecordid><originalsourceid>FETCH-LOGICAL-a671-f516427c4f001419cb596a05d94c75d05804494790c130a0f03de66bdedf95a3</originalsourceid><addsrcrecordid>eNotzssKwjAUBNBsXIj6Aa7MD7Tea5PULEV8geBC9-WahwbaRqKI_r3P1QwMDIexIUIuplLCmNIj3PMJAuaASmGXqRk3dHOnmIIP7xZiy31M_HZ2_BpOrbPcnFNs3ovhl1g_29gEqvus46m-usE_e2y_XBzm62y7W23ms21GqsTMS1RiUhrhAVCgNkepFYG0WphSWpBTEEKLUoPBAgg8FNYpdbTOei2p6LHR7_Xrri4pNJSe1cdfff3FC5DYP0E</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A categorification for the signed chromatic polynomial</title><source>arXiv.org</source><creator>Cheng, Zhiyun ; Lei, Ziyi ; Wang, Yitian ; Zhang, Yanguo</creator><creatorcontrib>Cheng, Zhiyun ; Lei, Ziyi ; Wang, Yitian ; Zhang, Yanguo</creatorcontrib><description>By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which corresponds to signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.</description><identifier>DOI: 10.48550/arxiv.2101.01661</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2021-01</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/2101.01661$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2101.01661$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Cheng, Zhiyun</creatorcontrib><creatorcontrib>Lei, Ziyi</creatorcontrib><creatorcontrib>Wang, Yitian</creatorcontrib><creatorcontrib>Zhang, Yanguo</creatorcontrib><title>A categorification for the signed chromatic polynomial</title><description>By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which corresponds to signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzssKwjAUBNBsXIj6Aa7MD7Tea5PULEV8geBC9-WahwbaRqKI_r3P1QwMDIexIUIuplLCmNIj3PMJAuaASmGXqRk3dHOnmIIP7xZiy31M_HZ2_BpOrbPcnFNs3ovhl1g_29gEqvus46m-usE_e2y_XBzm62y7W23ms21GqsTMS1RiUhrhAVCgNkepFYG0WphSWpBTEEKLUoPBAgg8FNYpdbTOei2p6LHR7_Xrri4pNJSe1cdfff3FC5DYP0E</recordid><startdate>20210105</startdate><enddate>20210105</enddate><creator>Cheng, Zhiyun</creator><creator>Lei, Ziyi</creator><creator>Wang, Yitian</creator><creator>Zhang, Yanguo</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210105</creationdate><title>A categorification for the signed chromatic polynomial</title><author>Cheng, Zhiyun ; Lei, Ziyi ; Wang, Yitian ; Zhang, Yanguo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-f516427c4f001419cb596a05d94c75d05804494790c130a0f03de66bdedf95a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Cheng, Zhiyun</creatorcontrib><creatorcontrib>Lei, Ziyi</creatorcontrib><creatorcontrib>Wang, Yitian</creatorcontrib><creatorcontrib>Zhang, Yanguo</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Cheng, Zhiyun</au><au>Lei, Ziyi</au><au>Wang, Yitian</au><au>Zhang, Yanguo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A categorification for the signed chromatic polynomial</atitle><date>2021-01-05</date><risdate>2021</risdate><abstract>By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which corresponds to signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.</abstract><doi>10.48550/arxiv.2101.01661</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2101.01661
ispartof
issn
language eng
recordid cdi_arxiv_primary_2101_01661
source arXiv.org
subjects Mathematics - Combinatorics
title A categorification for the signed chromatic polynomial
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T09%3A28%3A17IST&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=A%20categorification%20for%20the%20signed%20chromatic%20polynomial&rft.au=Cheng,%20Zhiyun&rft.date=2021-01-05&rft_id=info:doi/10.48550/arxiv.2101.01661&rft_dat=%3Carxiv_GOX%3E2101_01661%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