DP-4-colorability of planar graphs without adjacent cycles of given length

DP-4-colorability of planar graphs without adjacent cycles of given length

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k=3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycle...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete Applied Mathematics 2020-04, Vol.277, p.245-251
Hauptverfasser: Liu, Runrun, Li, Xiangwen, Nakprasit, Kittikorn, Sittitrai, Pongpat, Yu, Gexin
Format: Artikel
Sprache:eng
Schlagworte:
Coloring
Cycles
DP-colorings
Graphs
List colorings
Planar graphs
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 251
container_issue
container_start_page 245
container_title Discrete Applied Mathematics
container_volume 277
creator Liu, Runrun
Li, Xiangwen
Nakprasit, Kittikorn
Sittitrai, Pongpat
Yu, Gexin
description DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k=3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycles adjacent to triangles is DP-4-colorable for k=5,6, which implies that every planar graph G without k-cycles adjacent to triangles is 4-choosable for k=5,6. This extends the result of Kim and Ozeki on 3-, 5-, and 6-cycles.
doi_str_mv 10.1016/j.dam.2019.09.012
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2452921870</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0166218X1930438X</els_id><sourcerecordid>2452921870</sourcerecordid><originalsourceid>FETCH-LOGICAL-c368t-15ffbb69ecb455bed22bd168cb016569c64205b3646ecb893c4ff63b278996b23</originalsourceid><addsrcrecordid>eNp9kF9LwzAUxYMoOKcfwLeAz61J2qYNPsl0_mGgDwq-hSRNtpSuqUk22bc3ZT4LF-7L75x77gHgGqMcI0xvu7wV25wgzHKUBpMTMMNNTTJa1_gUzBJDM4Kbr3NwEUKHUEJwMwOvD-9ZmSnXOy-k7W08QGfg2ItBeLj2YtwE-GPjxu0iFG0nlB4iVAfV6zCBa7vXA-z1sI6bS3BmRB_01d-eg8_l48fiOVu9Pb0s7leZKmgTM1wZIyVlWsmyqqRuCZEtpo2SKWNFmaIlQZUsaEkT0rBClcbQQpK6YYxKUszBzdF39O57p0Pkndv5IZ3kpKwIS3_VKFH4SCnvQvDa8NHbrfAHjhGfKuMdT5XxqTKO0uDJ-e6o0Sn-3mrPg7J6ULq1XqvIW2f_Uf8CtZ5zWg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2452921870</pqid></control><display><type>article</type><title>DP-4-colorability of planar graphs without adjacent cycles of given length</title><source>Elsevier ScienceDirect Journals Complete</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Liu, Runrun ; Li, Xiangwen ; Nakprasit, Kittikorn ; Sittitrai, Pongpat ; Yu, Gexin</creator><creatorcontrib>Liu, Runrun ; Li, Xiangwen ; Nakprasit, Kittikorn ; Sittitrai, Pongpat ; Yu, Gexin</creatorcontrib><description>DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k=3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycles adjacent to triangles is DP-4-colorable for k=5,6, which implies that every planar graph G without k-cycles adjacent to triangles is 4-choosable for k=5,6. This extends the result of Kim and Ozeki on 3-, 5-, and 6-cycles.</description><identifier>ISSN: 0166-218X</identifier><identifier>EISSN: 1872-6771</identifier><identifier>DOI: 10.1016/j.dam.2019.09.012</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Coloring ; Cycles ; DP-colorings ; Graphs ; List colorings ; Planar graphs</subject><ispartof>Discrete Applied Mathematics, 2020-04, Vol.277, p.245-251</ispartof><rights>2019</rights><rights>Copyright Elsevier BV Apr 30, 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c368t-15ffbb69ecb455bed22bd168cb016569c64205b3646ecb893c4ff63b278996b23</citedby><cites>FETCH-LOGICAL-c368t-15ffbb69ecb455bed22bd168cb016569c64205b3646ecb893c4ff63b278996b23</cites><orcidid>0000-0001-9328-0766 ; 0000-0002-1770-8369</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.dam.2019.09.012$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Liu, Runrun</creatorcontrib><creatorcontrib>Li, Xiangwen</creatorcontrib><creatorcontrib>Nakprasit, Kittikorn</creatorcontrib><creatorcontrib>Sittitrai, Pongpat</creatorcontrib><creatorcontrib>Yu, Gexin</creatorcontrib><title>DP-4-colorability of planar graphs without adjacent cycles of given length</title><title>Discrete Applied Mathematics</title><description>DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k=3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycles adjacent to triangles is DP-4-colorable for k=5,6, which implies that every planar graph G without k-cycles adjacent to triangles is 4-choosable for k=5,6. This extends the result of Kim and Ozeki on 3-, 5-, and 6-cycles.</description><subject>Coloring</subject><subject>Cycles</subject><subject>DP-colorings</subject><subject>Graphs</subject><subject>List colorings</subject><subject>Planar graphs</subject><issn>0166-218X</issn><issn>1872-6771</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kF9LwzAUxYMoOKcfwLeAz61J2qYNPsl0_mGgDwq-hSRNtpSuqUk22bc3ZT4LF-7L75x77gHgGqMcI0xvu7wV25wgzHKUBpMTMMNNTTJa1_gUzBJDM4Kbr3NwEUKHUEJwMwOvD-9ZmSnXOy-k7W08QGfg2ItBeLj2YtwE-GPjxu0iFG0nlB4iVAfV6zCBa7vXA-z1sI6bS3BmRB_01d-eg8_l48fiOVu9Pb0s7leZKmgTM1wZIyVlWsmyqqRuCZEtpo2SKWNFmaIlQZUsaEkT0rBClcbQQpK6YYxKUszBzdF39O57p0Pkndv5IZ3kpKwIS3_VKFH4SCnvQvDa8NHbrfAHjhGfKuMdT5XxqTKO0uDJ-e6o0Sn-3mrPg7J6ULq1XqvIW2f_Uf8CtZ5zWg</recordid><startdate>20200430</startdate><enddate>20200430</enddate><creator>Liu, Runrun</creator><creator>Li, Xiangwen</creator><creator>Nakprasit, Kittikorn</creator><creator>Sittitrai, Pongpat</creator><creator>Yu, Gexin</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-9328-0766</orcidid><orcidid>https://orcid.org/0000-0002-1770-8369</orcidid></search><sort><creationdate>20200430</creationdate><title>DP-4-colorability of planar graphs without adjacent cycles of given length</title><author>Liu, Runrun ; Li, Xiangwen ; Nakprasit, Kittikorn ; Sittitrai, Pongpat ; Yu, Gexin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-15ffbb69ecb455bed22bd168cb016569c64205b3646ecb893c4ff63b278996b23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Coloring</topic><topic>Cycles</topic><topic>DP-colorings</topic><topic>Graphs</topic><topic>List colorings</topic><topic>Planar graphs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Runrun</creatorcontrib><creatorcontrib>Li, Xiangwen</creatorcontrib><creatorcontrib>Nakprasit, Kittikorn</creatorcontrib><creatorcontrib>Sittitrai, Pongpat</creatorcontrib><creatorcontrib>Yu, Gexin</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Discrete Applied Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Runrun</au><au>Li, Xiangwen</au><au>Nakprasit, Kittikorn</au><au>Sittitrai, Pongpat</au><au>Yu, Gexin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>DP-4-colorability of planar graphs without adjacent cycles of given length</atitle><jtitle>Discrete Applied Mathematics</jtitle><date>2020-04-30</date><risdate>2020</risdate><volume>277</volume><spage>245</spage><epage>251</epage><pages>245-251</pages><issn>0166-218X</issn><eissn>1872-6771</eissn><abstract>DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k=3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycles adjacent to triangles is DP-4-colorable for k=5,6, which implies that every planar graph G without k-cycles adjacent to triangles is 4-choosable for k=5,6. This extends the result of Kim and Ozeki on 3-, 5-, and 6-cycles.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.dam.2019.09.012</doi><tpages>7</tpages><orcidid>https://orcid.org/0000-0001-9328-0766</orcidid><orcidid>https://orcid.org/0000-0002-1770-8369</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0166-218X
ispartof Discrete Applied Mathematics, 2020-04, Vol.277, p.245-251
issn 0166-218X
1872-6771
language eng
recordid cdi_proquest_journals_2452921870
source Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals
subjects Coloring
Cycles
DP-colorings
Graphs
List colorings
Planar graphs
title DP-4-colorability of planar graphs without adjacent cycles of given length
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T04%3A42%3A52IST&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=DP-4-colorability%20of%20planar%20graphs%20without%20adjacent%20cycles%20of%20given%20length&rft.jtitle=Discrete%20Applied%20Mathematics&rft.au=Liu,%20Runrun&rft.date=2020-04-30&rft.volume=277&rft.spage=245&rft.epage=251&rft.pages=245-251&rft.issn=0166-218X&rft.eissn=1872-6771&rft_id=info:doi/10.1016/j.dam.2019.09.012&rft_dat=%3Cproquest_cross%3E2452921870%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=2452921870&rft_id=info:pmid/&rft_els_id=S0166218X1930438X&rfr_iscdi=true