Dynamic concentration of the triangle‐free process
The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates....
Uloženo v:
| Vydáno v: | Random structures & algorithms Ročník 58; číslo 2; s. 221 - 293 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
John Wiley & Sons, Inc
01.03.2021
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 triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R(3, t): we show R(3,t)>(1/4−o(1))t2/logt, which is within a 4 + o(1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self‐correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle‐free graph produced by the triangle‐free process: they are precisely those triangle‐free graphs with density at most 2. |
|---|---|
| AbstractList | The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R(3, t): we show R(3,t)>(1/4−o(1))t2/logt, which is within a 4 + o(1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self‐correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle‐free graph produced by the triangle‐free process: they are precisely those triangle‐free graphs with density at most 2. The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R (3, t ): we show , which is within a 4 + o (1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self‐correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle‐free graph produced by the triangle‐free process: they are precisely those triangle‐free graphs with density at most 2. The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R(3, t): we show R(3,t)>(1/4−o(1))t2/logt, which is within a 4 + o(1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self‐correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle‐free graph produced by the triangle‐free process: they are precisely those triangle‐free graphs with density at most 2. |
| Author | Keevash, Peter Bohman, Tom |
| Author_xml | – sequence: 1 givenname: Tom surname: Bohman fullname: Bohman, Tom email: tbohman@math.cmu.edu organization: Carnegie Mellon University – sequence: 2 givenname: Peter surname: Keevash fullname: Keevash, Peter organization: University of Oxford |
| BookMark | eNp1kL1OwzAUhS1UJNrAwBtEYmJI67_E8VgVCkiVkPiZLcfY4Cq1i50KZeMReEaeBPdnQjDdO3zn3HvOCAycdxqAcwTHCEI8CVGOMeSMHIEhgrwuMEX1YLtTXPCa4BMwinEJIWQEkyGgV72TK6ty5Z3Srguys97l3uTdm867YKV7bfX355cJWufr4JWO8RQcG9lGfXaYGXieXz_NbovF_c3dbLooFE4fFFpS03BCGYMlohJx01ScKYZUSXDZUGywrJWqVP0iNeGKYFNhhBppeFIhQzJwsfdNd983OnZi6TfBpZMCU1ZRXpeJzMBkT6ngYwzaCGW7XYyUxrYCQbGtRqRqxK6apLj8pVgHu5Kh_5M9uH_YVvf_g-LhcbpX_AAYrHU1 |
| CitedBy_id | crossref_primary_10_1002_rsa_21278 crossref_primary_10_1137_21M1437573 crossref_primary_10_1137_21M1444953 crossref_primary_10_1002_rsa_21284 crossref_primary_10_1017_S0963548325000124 crossref_primary_10_1002_rsa_21050 crossref_primary_10_1016_j_ejc_2024_104092 crossref_primary_10_1016_j_jctb_2025_08_001 crossref_primary_10_1112_plms_12400 crossref_primary_10_1016_j_ejc_2022_103551 crossref_primary_10_1016_j_ejc_2023_103872 crossref_primary_10_1016_j_disc_2022_113071 crossref_primary_10_1002_jgt_23180 crossref_primary_10_1002_jgt_22873 crossref_primary_10_1002_jgt_22973 crossref_primary_10_1017_S0963548322000360 crossref_primary_10_1017_S0963548324000105 crossref_primary_10_1112_blms_13040 crossref_primary_10_1137_23M1588706 crossref_primary_10_1016_j_jctb_2024_07_002 crossref_primary_10_1007_s00493_023_00023_w crossref_primary_10_1112_blms_13214 |
| Cites_doi | 10.1214/aop/1176996452 10.1016/j.aim.2009.02.018 10.1002/rsa.20444 10.1017/S0963548311000368 10.1016/j.aim.2015.04.015 10.1007/s00222-010-0247-x 10.37236/1496 10.1002/rsa.3240060217 10.1002/1098-2418(200101)18:1<61::AID-RSA5>3.0.CO;2-T 10.1002/rsa.20378 10.1002/jgt.20453 10.37236/93 10.1137/110824097 10.1007/s004930070014 10.37236/655 10.37236/1192 10.1002/0471722154 10.1016/0012-365X(83)90273-X 10.1017/CBO9781316339831 10.4153/CJM-1961-029-9 10.4310/JOC.2010.v1.n4.a5 10.1017/S0963548300000183 10.1002/rsa.20468 10.1016/0012-365X(77)90044-9 10.1016/0097-3165(90)90070-D 10.1002/rsa.20517 10.1016/j.disc.2011.08.008 10.1002/rsa.3240070302 10.1016/0097-3165(80)90030-8 |
| ContentType | Journal Article |
| Copyright | 2020 Wiley Periodicals LLC 2021 Wiley Periodicals LLC. |
| Copyright_xml | – notice: 2020 Wiley Periodicals LLC – notice: 2021 Wiley Periodicals LLC. |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1002/rsa.20973 |
| 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 | CrossRef Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1098-2418 |
| EndPage | 293 |
| ExternalDocumentID | 10_1002_rsa_20973 RSA20973 |
| Genre | article |
| GrantInformation_xml | – fundername: EPSRC funderid: EP/G056730/1 – fundername: ERC funderid: 647678; 239696 – fundername: NSF funderid: DMS‐1001638; DMS‐1100215 |
| 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-c2973-ea4fb934770514a19fb697c71c5325b42f2a8cc6c8dae39c32f6211baf99341f3 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 30 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000589923600001&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 10:51:36 EDT 2025 Tue Nov 18 21:33:45 EST 2025 Sat Nov 29 02:48:13 EST 2025 Wed Jan 22 16:32:25 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2973-ea4fb934770514a19fb697c71c5325b42f2a8cc6c8dae39c32f6211baf99341f3 |
| Notes | Funding information This research was supported by the NSF Grants, DMS‐1001638 and DMS‐1100215 (T.B.). ERC Grants, 647678 and 239696. EPSRC Grant, EP/G056730/1 (P.K.). ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2476498599 |
| PQPubID | 1016429 |
| PageCount | 73 |
| ParticipantIDs | proquest_journals_2476498599 crossref_citationtrail_10_1002_rsa_20973 crossref_primary_10_1002_rsa_20973 wiley_primary_10_1002_rsa_20973_RSA20973 |
| PublicationCentury | 2000 |
| PublicationDate | March 2021 2021-03-00 20210301 |
| PublicationDateYYYYMMDD | 2021-03-01 |
| PublicationDate_xml | – month: 03 year: 2021 text: March 2021 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Hoboken |
| PublicationTitle | Random structures & algorithms |
| PublicationYear | 2021 |
| Publisher | John Wiley & Sons, Inc Wiley Subscription Services, Inc |
| Publisher_xml | – name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc |
| References | 2011; 333 2015; 280 1990; 55 1980; 29 1997; 20 2020; 263 2000; 7 2000; 20 2010; 181 2014; 28 2011; 39 1961; 13 2011; 18 1995; 6 2014; 45 2014; 44 1995; 7 2010; 64 2010; 1 2000 2011; 20 2009; 221 2016 2001; 18 1994; 1 1992; 1 1983; 46 2009; 16 1975; 3 2009; 18 e_1_2_10_23_1 Fiz Pontiveros G. (e_1_2_10_14_1) 2020; 263 e_1_2_10_24_1 e_1_2_10_21_1 e_1_2_10_22_1 e_1_2_10_20_1 Bollobás B. (e_1_2_10_10_1) 2009 e_1_2_10_2_1 e_1_2_10_4_1 e_1_2_10_18_1 e_1_2_10_3_1 e_1_2_10_19_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_5_1 e_1_2_10_17_1 e_1_2_10_8_1 e_1_2_10_7_1 e_1_2_10_15_1 e_1_2_10_12_1 e_1_2_10_9_1 e_1_2_10_13_1 e_1_2_10_34_1 e_1_2_10_33_1 e_1_2_10_11_1 e_1_2_10_32_1 e_1_2_10_31_1 e_1_2_10_30_1 e_1_2_10_29_1 e_1_2_10_27_1 e_1_2_10_28_1 e_1_2_10_25_1 e_1_2_10_26_1 |
| References_xml | – volume: 263 start-page: 125 year: 2020 article-title: The triangle‐free process and (3, ) publication-title: Mem. Amer. Math. Soc. – volume: 20 start-page: 939 year: 2011 end-page: 955 article-title: The final size of the ‐free process publication-title: Combin. Probab. Comput. – volume: 55 start-page: 247 year: 1990 end-page: 255 article-title: Counting extensions publication-title: J. Combin. Theory Ser. A – volume: 333 start-page: 2703 year: 2011 end-page: 2707 article-title: Dense subgraphs in the H‐free process publication-title: Discrete Math. – volume: 3 start-page: 100 year: 1975 end-page: 118 article-title: On tail probabilities for martingales publication-title: Ann. Probab. – volume: 18 year: 2011 article-title: No dense subgraphs appear in the triangle‐free graph process publication-title: Electron. J. Combin. – year: 2000 – volume: 280 start-page: 379 year: 2015 end-page: 438 article-title: Random triangle removal publication-title: Adv. Math. – volume: 18 start-page: 15 year: 2009 end-page: 115 – volume: 64 start-page: 244 year: 2010 end-page: 249 article-title: A note on regular Ramsey Graphs publication-title: J. Graph Theory – volume: 16 year: 2009 article-title: Lower bounds for the size of random maximal H‐free graphs publication-title: Electron. J. Combin. – volume: 46 start-page: 83 year: 1983 end-page: 87 article-title: A note on the independence number of triangle‐free graphs publication-title: Discrete Math. – volume: 45 start-page: 513 year: 2014 end-page: 551 article-title: The diamond‐free process publication-title: Random Structures Algorithms – volume: 1 start-page: 477 year: 2010 end-page: 488 article-title: A note on the random greedy triangle‐packing algorithm publication-title: J. Combin. – year: 2016 – volume: 18 start-page: 61 year: 2001 end-page: 82 article-title: Random maximal ‐free graphs publication-title: Random Structures Algorithms – volume: 1 year: 1994 article-title: Explicit ramsey graphs and orthonormal labelings publication-title: Electron. J. Combin. – volume: 20 start-page: 69 year: 1997 end-page: 76 article-title: Asymptotic lower bounds for Ramsey functions publication-title: Discrete Math. – volume: 13 start-page: 346 year: 1961 end-page: 352 article-title: Graph theory and probability, II publication-title: Can. J. Math. – volume: 28 start-page: 1276 year: 2014 end-page: 1305 article-title: The final size of the ‐free process publication-title: SIAM Discrete Math. – volume: 44 start-page: 355 year: 2014 end-page: 397 article-title: When does the ‐free process stop? publication-title: Random Structures Algorithms – volume: 20 start-page: 417 year: 2000 end-page: 434 article-title: Concentration of multivariate polynomials and its applications publication-title: Combinatorica – volume: 181 start-page: 291 year: 2010 end-page: 336 article-title: The early evolution of the H‐free process publication-title: Invent. Math. – volume: 6 start-page: 309 year: 1995 end-page: 318 article-title: On the size of a random maximal graph publication-title: Random Structures Algorithms – volume: 221 start-page: 1653 year: 2009 end-page: 1677 article-title: The triangle‐free process publication-title: Adv. Math. – volume: 44 start-page: 490 year: 2014 end-page: 526 article-title: The ‐free process publication-title: Random Structures Algorithms – volume: 29 start-page: 354 year: 1980 end-page: 360 article-title: A note on Ramsey numbers publication-title: J. Combin. Theory Ser. A – volume: 1 start-page: 169 year: 1992 end-page: 180 article-title: Random graph processes with degree restrictions publication-title: Combin. Probab. Comput. – volume: 7 year: 2000 article-title: Constrained graph processes publication-title: Electron. J. Combin. – volume: 7 start-page: 173 year: 1995 end-page: 207 article-title: The Ramsey number (3, ) has order of magnitude publication-title: Random Structures Algorithms – volume: 39 start-page: 539 year: 2011 end-page: 543 article-title: Triangle‐free subgraphs in the triangle‐free process publication-title: Random Structures Algorithms – ident: e_1_2_10_15_1 doi: 10.1214/aop/1176996452 – ident: e_1_2_10_6_1 doi: 10.1016/j.aim.2009.02.018 – ident: e_1_2_10_33_1 – ident: e_1_2_10_31_1 doi: 10.1002/rsa.20444 – ident: e_1_2_10_22_1 doi: 10.1017/S0963548311000368 – ident: e_1_2_10_8_1 doi: 10.1016/j.aim.2015.04.015 – ident: e_1_2_10_9_1 doi: 10.1007/s00222-010-0247-x – ident: e_1_2_10_11_1 doi: 10.37236/1496 – ident: e_1_2_10_13_1 doi: 10.1002/rsa.3240060217 – ident: e_1_2_10_20_1 doi: 10.1002/1098-2418(200101)18:1<61::AID-RSA5>3.0.CO;2-T – ident: e_1_2_10_34_1 doi: 10.1002/rsa.20378 – ident: e_1_2_10_4_1 doi: 10.1002/jgt.20453 – ident: e_1_2_10_32_1 doi: 10.37236/93 – ident: e_1_2_10_23_1 doi: 10.1137/110824097 – ident: e_1_2_10_26_1 – ident: e_1_2_10_19_1 doi: 10.1007/s004930070014 – ident: e_1_2_10_17_1 doi: 10.37236/655 – volume: 263 start-page: 125 year: 2020 ident: e_1_2_10_14_1 article-title: The triangle‐free process and R(3, k) publication-title: Mem. Amer. Math. Soc. – ident: e_1_2_10_3_1 doi: 10.37236/1192 – ident: e_1_2_10_5_1 doi: 10.1002/0471722154 – ident: e_1_2_10_25_1 doi: 10.1016/0012-365X(83)90273-X – start-page: 15 volume-title: Handbook of Large‐scale Random Networks, Bolyai Soc. Math. Stud year: 2009 ident: e_1_2_10_10_1 – ident: e_1_2_10_16_1 doi: 10.1017/CBO9781316339831 – ident: e_1_2_10_12_1 doi: 10.4153/CJM-1961-029-9 – ident: e_1_2_10_7_1 doi: 10.4310/JOC.2010.v1.n4.a5 – ident: e_1_2_10_24_1 doi: 10.1017/S0963548300000183 – ident: e_1_2_10_30_1 doi: 10.1002/rsa.20468 – ident: e_1_2_10_27_1 doi: 10.1016/0012-365X(77)90044-9 – ident: e_1_2_10_28_1 doi: 10.1016/0097-3165(90)90070-D – ident: e_1_2_10_21_1 doi: 10.1002/rsa.20517 – ident: e_1_2_10_29_1 doi: 10.1016/j.disc.2011.08.008 – ident: e_1_2_10_18_1 doi: 10.1002/rsa.3240070302 – ident: e_1_2_10_2_1 doi: 10.1016/0097-3165(80)90030-8 |
| SSID | ssj0007323 |
| Score | 2.513313 |
| Snippet | The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no... The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 221 |
| SubjectTerms | Apexes dynamic concentration Graph theory Lower bounds Ramsey numbers triangle‐free Upper bounds |
| Title | Dynamic concentration of the triangle‐free process |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Frsa.20973 https://www.proquest.com/docview/2476498599 |
| Volume | 58 |
| WOSCitedRecordID | wos000589923600001&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 Full Collection 2020 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/eLvHCXMwpZ3NSgMxEICHWj3owX-xWmURD15Cu0m62eCpWIuHWqRa6W3JZhMRyrbsVs8-gs_ok5jsXxUUBG97mOyGyUwyWWa-ATinvgojwgjyuScRpZoh3hYYaU205IpE7SzL93HAhkN_MuF3Nbgsa2FyPkT1w816RrZfWwcXYdpaQkOT1GKDOCMrsIqN3dI6rPZG_fGg2ogZwXl-PcWIG8stwUJt3KoGfz-OljHm10g1O2r6W_-a5DZsFhGm081NYgdqKt6FjdsKz5ruAe3lfegdaYsW44Kc68y0Y4Qc28gjfpqqj7d3nSjlzPNagn0Y968frm5Q0T4BSduQCilBdcgJZcwyzoXLdehxJpkrOwR3Qoo1Fr6UnvQjoQiXBGvPXAdDoU3MQl1NDqAez2J1CA6JQs0FwzrEkVld4RPPtew2aUa5bSEacFFqMZAFW9y2uJgGORUZB0YRQaaIBpxVovMcqPGTULNciqDwqTTAlHmU-x3Ozecypf_-gmB0380ejv4uegzr2CasZAlmTagvkhd1AmvydfGcJqeFcX0CIPbSqg |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpZ1fS8MwEMCPuQnqg__F6dQiPvhS1iZZ04AvwzkmbkPmJnsraZqIMLqxTZ_9CH5GP4lJ23UKCoJvfbik5XKXXMPd7wAuiC_DCFNs-8wTNiGK2szhyFYKK8Ekjpwky_exTbtdfzhk9wW4WtTCpHyI_MLNeEayXxsHNxfS1SU1dDoz3CBG8QqUiDajWhFKjV5z0M53YopRmmBPkM206S7IQg6q5oO_n0fLIPNrqJqcNc2t_33lNmxmMaZVT41iBwoy3oWNTg5one0BaaSd6C1hyhbjjJ1rjZWlhSzTyiN-GsmPt3c1ldKapNUE-zBo3vSvW3bWQMEWpiWVLTlRIcOEUkM55y5ToceooK6oYVQLCVKI-0J4wo-4xExgpDz9QxhypaMW4ip8AMV4HMtDsHAUKsYpUiGK9PpyH3uuobcJPcp1OC_D5UKNgcjo4qbJxShIucgo0IoIEkWU4TwXnaRIjZ-EKou1CDKvmgWIUI8wv8aYfl2i9d8nCHoP9eTh6O-iZ7DW6nfaQfu2e3cM68ikryTpZhUozqcv8gRWxev8eTY9zSztE8aR1po |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpZ1fS8MwEMCPuYnog__F6dQiPvhStiZZ04Avw1kU5xjTyd5KmiYijG5s02c_gp_RT2LSf1NQEHzrw6UNl7vkUu5-B3BGPBlGmGLbY66wCVHUZg2ObKWwEkziqJFk-T52aLfrDYesV4KLvBYm5UMUP9yMZyT7tXFwOYlUfUENnc4MN4hRvAQV0mSudstKu-8POsVOTDFKE-wJspk23Zws1ED1YvD382gRZH4NVZOzxt_43yw3YT2LMa1WahRbUJLxNqzdFYDW2Q6QdtqJ3hKmbDHO2LnWWFlayDKtPOKnkfx4e1dTKa1JWk2wCwP_6uHy2s4aKNjCtKSyJScqZJhQaijn3GEqdBkV1BFNjJohQQpxTwhXeBGXmAmMlKsvhCFXOmohjsJ7UI7HsdwHC0ehYpwiFaJIry_3sOsYepvQo5wG51U4z9UYiIwubppcjIKUi4wCrYggUUQVTgvRSYrU-Emolq9FkHnVLECEuoR5Tcb05xKt__6CoH_fSh4O_i56Aiu9th90brq3h7CKTPZKkm1Wg_J8-iKPYFm8zp9n0-PM0D4BjsPWFQ |
| 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=Dynamic+concentration+of+the+triangle%E2%80%90free+process&rft.jtitle=Random+structures+%26+algorithms&rft.au=Bohman%2C+Tom&rft.au=Keevash%2C+Peter&rft.date=2021-03-01&rft.issn=1042-9832&rft.eissn=1098-2418&rft.volume=58&rft.issue=2&rft.spage=221&rft.epage=293&rft_id=info:doi/10.1002%2Frsa.20973&rft.externalDBID=n%2Fa&rft.externalDocID=10_1002_rsa_20973 |
| 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 |