The Johansson‐Molloy theorem for DP‐coloring
The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for triangle‐free graphs G, avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit...
Uloženo v:
| Vydáno v: | Random structures & algorithms Ročník 54; číslo 4; s. 653 - 664 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
John Wiley & Sons, Inc
01.07.2019
Wiley Subscription Services, Inc |
| Témata: | |
| ISSN: | 1042-9832, 1098-2418 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for triangle‐free graphs G, avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit in a somewhat unusual setting). On the other hand, we extend Molloy's result to DP‐coloring (also known as correspondence coloring), a generalization of list coloring introduced recently by Dvořák and Postle. |
|---|---|
| AbstractList | The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for triangle‐free graphs G, avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit in a somewhat unusual setting). On the other hand, we extend Molloy's result to DP‐coloring (also known as correspondence coloring), a generalization of list coloring introduced recently by Dvořák and Postle. The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound for triangle‐free graphs G , avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit in a somewhat unusual setting). On the other hand, we extend Molloy's result to DP‐coloring (also known as correspondence coloring), a generalization of list coloring introduced recently by Dvořák and Postle. |
| Author | Bernshteyn, Anton |
| Author_xml | – sequence: 1 givenname: Anton surname: Bernshteyn fullname: Bernshteyn, Anton email: bernsht2@illinois.edu organization: University of Illinois at Urbana‐Champaign |
| BookMark | eNp9kE1OwzAQhS0EEm1hwQ0isWKRduw4drKsyr-KQFDWlpOMaarULnYq1B1H4IychJSyQoLVG42-90bz-mTfOouEnFAYUgA28kEPGWSU7pEehTyLGafZ_nbmLM6zhB2SfggLAJAJS3oEZnOMbt1c2xCc_Xz_uHNN4zZRO0fncRkZ56Pzh25fusb52r4ckQOjm4DHPzogz5cXs8l1PL2_upmMp3HJcknjpKBFlUqkudBVKXIqkINktBQZMm4MdgpViYUATLEAaqoiqyoupeQmFSwZkNNd7sq71zWGVi3c2tvupGKMiYTTtHtnQM52VOldCB6NWvl6qf1GUVDbQlRXiPoupGNHv9iybnVbO9t6XTf_Od7qBjd_R6vHp_HO8QXUKnSL |
| CitedBy_id | crossref_primary_10_1007_s00373_023_02721_0 crossref_primary_10_1137_21M1437573 crossref_primary_10_1016_j_jctb_2023_02_004 crossref_primary_10_1016_j_aam_2020_102131 crossref_primary_10_1002_rsa_70000 crossref_primary_10_1002_rsa_70012 crossref_primary_10_1007_s00373_023_02633_z crossref_primary_10_1007_s00373_022_02520_z crossref_primary_10_1016_j_jctb_2022_06_002 crossref_primary_10_4153_S0008439521001004 crossref_primary_10_1016_j_disc_2018_08_003 crossref_primary_10_1017_S0963548322000104 crossref_primary_10_1016_j_ejc_2023_103750 crossref_primary_10_1016_j_disc_2022_113093 crossref_primary_10_1016_j_ejc_2023_103890 crossref_primary_10_1002_jgt_22796 crossref_primary_10_1007_s00026_025_00778_7 crossref_primary_10_1016_j_disc_2021_112306 crossref_primary_10_1002_rsa_20945 crossref_primary_10_1016_j_disc_2023_113779 crossref_primary_10_1016_j_disc_2021_112765 crossref_primary_10_1016_j_disc_2020_112115 crossref_primary_10_3103_S1055134419030039 |
| Cites_doi | 10.2298/AADM160411008B 10.1016/j.ejc.2013.02.007 10.1137/S0097539793250767 10.1002/rsa.20411 10.1016/j.disc.2016.05.012 10.1006/jctb.1999.1910 10.1007/s00493-015-3070-6 10.1002/rsa.3240070305 10.1017/S0963548301004758 10.1016/j.ic.2014.12.018 10.1002/0471722154 10.1016/j.disc.2012.11.011 10.1002/(SICI)1097-0118(199906)31:2<149::AID-JGT8>3.0.CO;2-# |
| ContentType | Journal Article |
| Copyright | 2018 Wiley Periodicals, Inc. 2019 Wiley Periodicals, Inc. |
| Copyright_xml | – notice: 2018 Wiley Periodicals, Inc. – notice: 2019 Wiley Periodicals, Inc. |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1002/rsa.20811 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1098-2418 |
| EndPage | 664 |
| ExternalDocumentID | 10_1002_rsa_20811 RSA20811 |
| Genre | article |
| GrantInformation_xml | – fundername: Illinois Distinguished Fellowship |
| GroupedDBID | -~X .3N .4S .DC .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABEML ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCFJ ACCZN ACGFO ACGFS ACIWK ACPOU ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFWVQ AFZJQ AHBTC AIAGR AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE FSPIC G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ H~9 IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6L MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RX1 SAMSI SUPJJ TN5 TUS UB1 V2E V8K W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WRC WWM WXSBR WYISQ XBAML XG1 XPP XSW XV2 ZZTAW ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGQPQ AGXDD AGYGG AIDQK AIDYY AIQQE AMVHM CITATION O8X 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c2971-3b1bd57e196adc6916e40721c68e24ffe68e0dceb60e5eb01fdb8dd47774f5623 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 29 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000470931400003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1042-9832 |
| IngestDate | Fri Jul 25 12:09:48 EDT 2025 Tue Nov 18 19:44:30 EST 2025 Sat Nov 29 02:48:13 EST 2025 Wed Jan 22 16:48:44 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2971-3b1bd57e196adc6916e40721c68e24ffe68e0dceb60e5eb01fdb8dd47774f5623 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2226341598 |
| PQPubID | 1016429 |
| PageCount | 1 |
| ParticipantIDs | proquest_journals_2226341598 crossref_primary_10_1002_rsa_20811 crossref_citationtrail_10_1002_rsa_20811 wiley_primary_10_1002_rsa_20811_RSA20811 |
| PublicationCentury | 2000 |
| PublicationDate | July 2019 2019-07-00 20190701 |
| PublicationDateYYYYMMDD | 2019-07-01 |
| PublicationDate_xml | – month: 07 year: 2019 text: July 2019 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Hoboken |
| PublicationTitle | Random structures & algorithms |
| PublicationYear | 2019 |
| Publisher | John Wiley & Sons, Inc Wiley Subscription Services, Inc |
| Publisher_xml | – name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc |
| References | 2010; 10 29 2000 2016; 339 2013; 34 1979; XXVI 1997; 26 2013; 313 2015; 243 2013; 42 1999; 77 1999; 31 2016; 36 2001; 10 1995; 7 e_1_2_7_6_1 e_1_2_7_5_1 e_1_2_7_4_1 e_1_2_7_3_1 e_1_2_7_9_1 e_1_2_7_8_1 e_1_2_7_7_1 e_1_2_7_19_1 e_1_2_7_18_1 e_1_2_7_17_1 e_1_2_7_16_1 e_1_2_7_2_1 e_1_2_7_15_1 e_1_2_7_14_1 e_1_2_7_13_1 e_1_2_7_12_1 e_1_2_7_11_1 V.G. Vizing (e_1_2_7_20_1); 29 P. Erdös (e_1_2_7_10_1) 1979 |
| References_xml | – volume: 10 start-page: 73 year: 2010 end-page: 87 article-title: Harmonious coloring of uniform hypergraphs publication-title: Applic. Anal. Disc. Math. – volume: 313 start-page: 517 year: 2013 end-page: 539 article-title: Colorings of plane graphs: a survey publication-title: Disc. Math. – volume: 26 start-page: 350 issue: 2 year: 1997 end-page: 368 article-title: Randomized distributed edge coloring via an extension of the Chernoff‐Hoeffding bounds publication-title: SIAM J. Comput – volume: 243 start-page: 263 year: 2015 end-page: 280 article-title: Distributed coloring algorithms for triangle‐free graphs publication-title: Inform. Comput. – volume: 29 start-page: 3 end-page: 10 article-title: (Russian), [Vertex colorings with given colors] publication-title: Metody Diskret. Analiz. – year: 2000 – volume: 339 start-page: 2680 year: 2016 end-page: 2692 article-title: The asymptotic behavior of the correspondence chromatic number publication-title: Disc. Math. – volume: XXVI start-page: 125 year: 1979 end-page: 157 – volume: 7 start-page: 269 issue: 3 year: 1995 end-page: 271 article-title: On the independence number of sparse graphs publication-title: Rand. Struct. Algor. – volume: 10 start-page: 345 year: 2001 end-page: 347 article-title: A note on vertex list colouring publication-title: Combin. Prob. Comput. – volume: 31 start-page: 149 year: 1999 end-page: 153 article-title: The list colouring constants publication-title: J. Graph Theory – volume: 77 start-page: 73 year: 1999 end-page: 82 article-title: Coloring graphs with sparse neighborhoods publication-title: J. Comb. Theory, Ser. – volume: 34 start-page: 1019 issue: 6 year: 2013 end-page: 1027 article-title: Acyclic edge‐coloring using entropy compression publication-title: Eur. J. Combin. – volume: 42 start-page: 214 issue: 2 year: 2013 end-page: 225 article-title: New approach to nonrepetitive sequences publication-title: Rand. Struct. Alg. – volume: 36 start-page: 661 year: 2016 end-page: 686 article-title: Nonrepetitive colouring via entropy compression publication-title: Combinatorica – ident: e_1_2_7_4_1 doi: 10.2298/AADM160411008B – ident: e_1_2_7_8_1 – start-page: 125 volume-title: Proc. West Coast Conf. on Combinatorics, Graph Theory and Computing, Congressus Numerantium year: 1979 ident: e_1_2_7_10_1 – ident: e_1_2_7_9_1 doi: 10.1016/j.ejc.2013.02.007 – ident: e_1_2_7_15_1 doi: 10.1137/S0097539793250767 – ident: e_1_2_7_13_1 – ident: e_1_2_7_11_1 doi: 10.1002/rsa.20411 – ident: e_1_2_7_14_1 – ident: e_1_2_7_5_1 doi: 10.1016/j.disc.2016.05.012 – ident: e_1_2_7_19_1 – ident: e_1_2_7_2_1 doi: 10.1006/jctb.1999.1910 – volume: 29 start-page: 3 ident: e_1_2_7_20_1 article-title: (Russian), [Vertex colorings with given colors] publication-title: Metody Diskret. Analiz. – ident: e_1_2_7_7_1 doi: 10.1007/s00493-015-3070-6 – ident: e_1_2_7_18_1 doi: 10.1002/rsa.3240070305 – ident: e_1_2_7_12_1 doi: 10.1017/S0963548301004758 – ident: e_1_2_7_16_1 doi: 10.1016/j.ic.2014.12.018 – ident: e_1_2_7_3_1 doi: 10.1002/0471722154 – ident: e_1_2_7_6_1 doi: 10.1016/j.disc.2012.11.011 – ident: e_1_2_7_17_1 doi: 10.1002/(SICI)1097-0118(199906)31:2<149::AID-JGT8>3.0.CO;2-# |
| SSID | ssj0007323 |
| Score | 2.4637992 |
| Snippet | The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for... The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound for triangle‐free graphs G , avoiding the... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 653 |
| SubjectTerms | Coloring DP‐coloring entropy compression Graph coloring list coloring Local Lemma triangle‐free graphs |
| Title | The Johansson‐Molloy theorem for DP‐coloring |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Frsa.20811 https://www.proquest.com/docview/2226341598 |
| Volume | 54 |
| WOSCitedRecordID | wos000470931400003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library customDbUrl: eissn: 1098-2418 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007323 issn: 1042-9832 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NS8NAEB1K60EPfovVKkE8eAlNtkk2i6diLSJtKdVCbyH7ERS0laYK3vwJ_kZ_ibPZJFVQELwkIUyyYfJm5rHsvAU4lZj1fOl4tucpPFBX2LGrhVyFyyUNZUyNzmyPDgbhZMKGFTgvemGMPkQ54aYjI8vXOsBjnjaXoqHzVMsGhbqvt0YQt14Vap1Rd9wrEzFtEbO-3iM2Q-QWwkIOaZYPfy9HS475lalmpaa78a-P3IT1nGFabQOJLaio6Tas9Ut51nQHHASHdT27wzKFdPvj7b2PaJi9Wqar8dFCImt1hnhfS1rrib9dGHcvby-u7HzrBFsQRl27xdHVPlUYX7EUAXJAlSmhiSBUxEsShWdHCsUDR_mKO24ieSilR5ENJpoS7UF1OpuqfbC8mCEL4kRJLOdu7PJYKkFoRl1CFrA6nBUejESuK663t3iIjCIyidAJUeaEOpyUpk9GTOMno0bxG6I8ntIIWUyA9dZnIQ6XOfz3F0Sjm3Z2cfB300NYRSbEzDrcBlQX82d1BCviZXGfzo9zYH0CrorQ5Q |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NS8NAEB1KK6gHv8Vq1SAevIQm6SabBS_FWqqmpdQWegvJ7gYFbaWpgjd_gr_RX-JsvqqgIHhJQphkw-TNzmPYeQtwKnDWs4VBdEIkHqjJ9cBUQq7cDAV1RUBTnVmP9nrueMz6JTjPe2FSfYii4KYiI5mvVYCrgnR9oRo6i5VukKsaeysEYWSXodIatEdeMRPThpUusCeWzhC6ubKQYdWLh7_nowXJ_EpVk1zTXv_fV27AWsYxtWYKik0oyckWrHYLgdZ4GwyEh3Y9vcNEhYT74-29i3iYvmppX-OjhlRWa_XxvhK1VqW_HRi1L4cXHT3bPEHnFqOm3gjR2TaVGGGB4A6yQJlooXHHlRaJIolnQ3AZOoa0ZWiYkQhdIQhFPhgpUrQL5cl0IvdAIwFDHhRaUmBCNwMzDITkFk3Ii8scVoWz3IU-z5TF1QYXD36qiWz56AQ_cUIVTgrTp1RO4yejWv4f_CyiYh95jIMZ12YuDpd4_PcX-IPbZnKx_3fTY1juDLue7131bg5gBXkRS1fl1qA8nz3LQ1jiL_P7eHaUoewTOVrU1Q |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFA7DieiDd3E6tYgPvpS1Wdo04MtwFi_bGNPB3kKbpCjoNtYp-OZP8Df6Szxpuk5BQfClLeW0KV_P5SPkfEHoRELW86RDbEIUHKgr7MjVQq7CjSUNZESNzmyLdjrBYMC6JXQ264Ux-hDFhJuOjCxf6wBXY5nU5qqhk1TrBgW6sbdMPOZDWJabvbDfKjIxrWOzwJ5gm4HrzpSFHFwrHv5ej-Yk8ytVzWpNuPa_r1xHqznHtBrGKTZQSQ030Uq7EGhNt5AD7mFdj-6hUAHh_nh7b4M_jF4t09f4ZAGVtZpduK9FrfXU3zbqhxd355d2vnmCLTCjrl2PAWyPKoiwSAofWKDKtNCEHyhMkkTB2ZFCxb6jPBU7biLjQEpCgQ8mmhTtoIXhaKh2kUUiABfHWEko6G7kxpFUAtOMvATMZxV0OoOQi1xZXG9w8ciNJjLmAALPQKig48J0bOQ0fjKqzv4DzyMq5cBjfKi4HgtguAzx31_Ae7eN7GLv76ZHaKnbDHnrqnOzj5aBFjGzKLeKFqaTZ3WAFsXL9CGdHOZO9gkEANRQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+Johansson%E2%80%90Molloy+theorem+for+DP%E2%80%90coloring&rft.jtitle=Random+structures+%26+algorithms&rft.au=Bernshteyn%2C+Anton&rft.date=2019-07-01&rft.issn=1042-9832&rft.eissn=1098-2418&rft.volume=54&rft.issue=4&rft.spage=653&rft.epage=664&rft_id=info:doi/10.1002%2Frsa.20811&rft.externalDBID=n%2Fa&rft.externalDocID=10_1002_rsa_20811 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1042-9832&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1042-9832&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1042-9832&client=summon |