Some sharp results on the generalized Turán numbers
For graphs T,H, let ex(n,T,H) denote the maximum number of copies of T in an n-vertex H-free graph. In this paper we prove some sharp results on this generalization of Turán numbers, where our focus is for the graphs T,H satisfying χ(T)<χ(H). This can be dated back to Erdős (1962), where he gener...
Saved in:
| Published in | European journal of combinatorics Vol. 84; p. 103026 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.02.2020
|
| Online Access | Get full text |
| ISSN | 0195-6698 1095-9971 |
| DOI | 10.1016/j.ejc.2019.103026 |
Cover
| Abstract | For graphs T,H, let ex(n,T,H) denote the maximum number of copies of T in an n-vertex H-free graph. In this paper we prove some sharp results on this generalization of Turán numbers, where our focus is for the graphs T,H satisfying χ(T)<χ(H). This can be dated back to Erdős (1962), where he generalized the celebrated Turán’s theorem by showing that for any r≥m, the Turán graph Tr(n) uniquely attains ex(n,Km,Kr+1). For general graphs H with χ(H)=r+1>m, Alon and Shikhelman (2016) showed that ex(n,Km,H)=rm(nr)m+o(nm). Here we determine this error term o(nm) up to a constant factor. We prove that ex(n,Km,H)=rm(nr)m+biex(n,H)⋅Θ(nm−2), where biex(n,H) is the Turán number of the decomposition family of H. As a special case, we extend Erdős’ result, by showing that Tr(n) uniquely attains ex(n,Km,H) for any edge-critical graph H. We also consider T being non-clique, where even the simplest case seems to be intricate. Following from a more general result, we show that for all s≤t, T2(n) maximizes the number of Ks,t in n-vertex triangle-free graphs if and only if t<s+12+2s+14. |
|---|---|
| AbstractList | For graphs T,H, let ex(n,T,H) denote the maximum number of copies of T in an n-vertex H-free graph. In this paper we prove some sharp results on this generalization of Turán numbers, where our focus is for the graphs T,H satisfying χ(T)<χ(H). This can be dated back to Erdős (1962), where he generalized the celebrated Turán’s theorem by showing that for any r≥m, the Turán graph Tr(n) uniquely attains ex(n,Km,Kr+1). For general graphs H with χ(H)=r+1>m, Alon and Shikhelman (2016) showed that ex(n,Km,H)=rm(nr)m+o(nm). Here we determine this error term o(nm) up to a constant factor. We prove that ex(n,Km,H)=rm(nr)m+biex(n,H)⋅Θ(nm−2), where biex(n,H) is the Turán number of the decomposition family of H. As a special case, we extend Erdős’ result, by showing that Tr(n) uniquely attains ex(n,Km,H) for any edge-critical graph H. We also consider T being non-clique, where even the simplest case seems to be intricate. Following from a more general result, we show that for all s≤t, T2(n) maximizes the number of Ks,t in n-vertex triangle-free graphs if and only if t<s+12+2s+14. |
| ArticleNumber | 103026 |
| Author | Qiu, Yu Ma, Jie |
| Author_xml | – sequence: 1 givenname: Jie orcidid: 0000-0002-0095-255X surname: Ma fullname: Ma, Jie email: jiema@ustc.edu.cn – sequence: 2 givenname: Yu surname: Qiu fullname: Qiu, Yu email: yuqiu@mail.ustc.edu.cn |
| BookMark | eNp9j0tOwzAQhi1UJNrCAdj5Agl24ti1WKGKl1SJBWVt-TGhjlKnslMkuA1n4WK4KisWXY1Go2_-_5uhSRgCIHRNSUkJ5TddCZ0tK0Jl3mtS8TM0pUQ2hZSCTtA0H5qCc7m4QLOUOkIobep6itjrsAWcNjrucIS078eEh4DHDeB3CBB177_A4fU-_nwHHPZbAzFdovNW9wmu_uYcvT3cr5dPxerl8Xl5typsJcVYWMZyuKFUa26EdJWoTGUbIG5hhLNacMnAMVKDycVqZ02rLW1awzTTVPB6jujxr41DShFatYt-q-OnokQdtFWnsrY6aKujdmbEP8b6UY9-CGPUvj9J3h5JyEofHqJK1kOw4HwEOyo3-BP0L1wUdLw |
| CitedBy_id | crossref_primary_10_1016_j_aam_2024_102740 crossref_primary_10_1016_j_disc_2023_113355 crossref_primary_10_1007_s40840_023_01602_2 crossref_primary_10_1007_s40840_022_01412_y crossref_primary_10_1007_s10474_023_01340_8 crossref_primary_10_1016_j_ejc_2023_103793 crossref_primary_10_1556_012_2023_01533 crossref_primary_10_1007_s00373_021_02329_2 crossref_primary_10_1016_j_ejc_2021_103350 crossref_primary_10_1016_j_disc_2021_112509 crossref_primary_10_1002_jgt_23210 crossref_primary_10_1007_s00373_024_02876_4 crossref_primary_10_1017_S0963548321000560 crossref_primary_10_1137_19M1239052 crossref_primary_10_1007_s00373_024_02757_w crossref_primary_10_1002_jgt_22723 crossref_primary_10_1016_j_disc_2021_112445 crossref_primary_10_1016_j_disc_2024_114149 crossref_primary_10_1016_j_disc_2023_113710 crossref_primary_10_1016_j_ejc_2022_103519 crossref_primary_10_1016_j_disc_2024_114015 crossref_primary_10_1360_SSM_2023_0201 crossref_primary_10_1002_jgt_23151 crossref_primary_10_1016_j_ejc_2022_103682 crossref_primary_10_1016_j_ejc_2019_103057 crossref_primary_10_1016_j_jctb_2023_06_004 crossref_primary_10_1002_jgt_22652 crossref_primary_10_1016_j_ejc_2025_104135 crossref_primary_10_4153_S0008414X21000316 crossref_primary_10_1007_s00373_022_02518_7 crossref_primary_10_1016_j_disc_2023_113866 crossref_primary_10_1016_j_disc_2024_114219 crossref_primary_10_1007_s00373_021_02403_9 crossref_primary_10_1016_j_disc_2023_113863 crossref_primary_10_1016_j_jctb_2020_05_005 crossref_primary_10_1016_j_disc_2022_112997 |
| Cites_doi | 10.1007/BF02579292 10.1016/j.jctb.2014.03.001 10.1016/j.jcta.2017.10.002 10.1016/j.jctb.2012.04.001 10.1016/j.jctb.2015.05.001 10.1016/j.disc.2003.11.007 10.1016/j.jctb.2016.03.004 10.4064/cm-3-1-50-57 10.1016/j.jcta.2012.12.008 10.1017/S0963548317000542 10.1016/j.disc.2017.12.018 10.1016/0012-365X(74)90133-2 10.1002/jgt.3190180610 10.1017/S0963548311000629 10.1007/BF01789461 10.1016/j.jctb.2017.08.005 10.1016/j.disc.2007.08.016 |
| ContentType | Journal Article |
| Copyright | 2019 Elsevier Ltd |
| Copyright_xml | – notice: 2019 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ejc.2019.103026 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1095-9971 |
| ExternalDocumentID | 10_1016_j_ejc_2019_103026 S0195669819301271 |
| GrantInformation_xml | – fundername: Anhui Initiative in Quantum Information Technologies, China grantid: AHY150200 – fundername: National Natural Science Foundation of China grantid: 11501539; 1 funderid: http://dx.doi.org/10.13039/501100001809 |
| GroupedDBID | --K --M -ET -~X .~1 0R~ 1B1 1RT 1~. 1~5 29G 4.4 457 4G. 5GY 5VS 6I. 6OB 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AASFE AAXUO ABAOU ABFNM ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADFGL ADIYS ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ H~9 IHE IXB J1W KOM LG5 M25 M41 MCRUF MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K WUQ XPP ZMT ZU3 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH |
| ID | FETCH-LOGICAL-c297t-c44971b11aa6b79d272b2c5e0d8b7dca7694ed403eb6983dcbfac15fb4a4a1763 |
| IEDL.DBID | AIKHN |
| ISSN | 0195-6698 |
| IngestDate | Tue Jul 01 01:37:05 EDT 2025 Thu Apr 24 23:01:05 EDT 2025 Fri Feb 23 02:17:14 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c297t-c44971b11aa6b79d272b2c5e0d8b7dca7694ed403eb6983dcbfac15fb4a4a1763 |
| ORCID | 0000-0002-0095-255X |
| ParticipantIDs | crossref_primary_10_1016_j_ejc_2019_103026 crossref_citationtrail_10_1016_j_ejc_2019_103026 elsevier_sciencedirect_doi_10_1016_j_ejc_2019_103026 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | February 2020 2020-02-00 |
| PublicationDateYYYYMMDD | 2020-02-01 |
| PublicationDate_xml | – month: 02 year: 2020 text: February 2020 |
| PublicationDecade | 2020 |
| PublicationTitle | European journal of combinatorics |
| PublicationYear | 2020 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Erdős (b10) 1962; 7 Simonovits (b28) 1968 Győri, Pach, Simonovits (b22) 1991; 7 Alon, Kostochka, Shikhelman (b2) 2018; 9 Füredi (b14) 2015; 115 Erdős, Simonovits (b12) 1966; 1 Grzesik (b20) 2012; 102 Erdős (b11) 1968 Diestel (b7) 2006 Hatami, Hladký, Král, Norine, Razborov (b23) 2013; 120 Alon, Shikhelman (b3) 2016; 121 D. Gerbner, A. Methuku, M. Vizer, Generalized Turán problems for disjoint copies of graphs Loh, Tait, Timmons, Zhou (b25) 2018; 27 Luo (b26) 2018; 128 Szemerédi (b29) 1978 Bollobás, Győri (b5) 2008; 308 Eckhoff (b8) 2004; 282 L. Gishboliner, A. Shapira, A generalized Turán problem and its applications . D. Gerbner, B. Keszegh, C. Palmer, B. Patkós, On the number of cycles in a graph with restricted cycle lengths Allen, Böttcher, Person (b1) 2014; 108 Brown, Sidorenko (b6) 1994; 18 Erdős, Simonovits (b13) 1983; 3 Ma, Yuan, Zhang (b27) 2018; 154 Füredi, Kostochka, Luo (b15) 2018; 341 P. Erdős, Some recent results on extremal problems in graph theory, in: Theory of Graphs, International Symp. Rome, 1966, pp. 118–123. Kövári, Sós, Turán (b24) 1954; 3 Andrásfai, Erdős, Sós (b4) 1974; 8 D. Gerbner, E. Győri, A. Methuku, M. Vizer, Generalized Turán problems for even cycles Győri, Li (b21) 2012; 21 Turán (b30) 1941; 48 Ma (10.1016/j.ejc.2019.103026_b27) 2018; 154 Alon (10.1016/j.ejc.2019.103026_b2) 2018; 9 Allen (10.1016/j.ejc.2019.103026_b1) 2014; 108 Győri (10.1016/j.ejc.2019.103026_b22) 1991; 7 Erdős (10.1016/j.ejc.2019.103026_b11) 1968 Bollobás (10.1016/j.ejc.2019.103026_b5) 2008; 308 Brown (10.1016/j.ejc.2019.103026_b6) 1994; 18 Loh (10.1016/j.ejc.2019.103026_b25) 2018; 27 Szemerédi (10.1016/j.ejc.2019.103026_b29) 1978 Alon (10.1016/j.ejc.2019.103026_b3) 2016; 121 Erdős (10.1016/j.ejc.2019.103026_b12) 1966; 1 Füredi (10.1016/j.ejc.2019.103026_b15) 2018; 341 Grzesik (10.1016/j.ejc.2019.103026_b20) 2012; 102 Luo (10.1016/j.ejc.2019.103026_b26) 2018; 128 Kövári (10.1016/j.ejc.2019.103026_b24) 1954; 3 10.1016/j.ejc.2019.103026_b18 10.1016/j.ejc.2019.103026_b19 Füredi (10.1016/j.ejc.2019.103026_b14) 2015; 115 10.1016/j.ejc.2019.103026_b16 10.1016/j.ejc.2019.103026_b17 Győri (10.1016/j.ejc.2019.103026_b21) 2012; 21 Turán (10.1016/j.ejc.2019.103026_b30) 1941; 48 Erdős (10.1016/j.ejc.2019.103026_b10) 1962; 7 Andrásfai (10.1016/j.ejc.2019.103026_b4) 1974; 8 Diestel (10.1016/j.ejc.2019.103026_b7) 2006 Hatami (10.1016/j.ejc.2019.103026_b23) 2013; 120 Eckhoff (10.1016/j.ejc.2019.103026_b8) 2004; 282 Erdős (10.1016/j.ejc.2019.103026_b13) 1983; 3 10.1016/j.ejc.2019.103026_b9 Simonovits (10.1016/j.ejc.2019.103026_b28) 1968 |
| References_xml | – volume: 18 start-page: 629 year: 1994 end-page: 645 ident: b6 article-title: The inducibility of complete bipartite graphs publication-title: J. Graph Theory – volume: 121 start-page: 146 year: 2016 end-page: 172 ident: b3 article-title: Many publication-title: J. Combin. Theory Ser. B – reference: D. Gerbner, E. Győri, A. Methuku, M. Vizer, Generalized Turán problems for even cycles, – volume: 108 start-page: 92 year: 2014 end-page: 101 ident: b1 article-title: An improved error term for minimal publication-title: J. Combin. Theory Ser. B – start-page: 279 year: 1968 end-page: 319 ident: b28 article-title: A method for solving extremal problems in graph theory, stability problems publication-title: Theory of Graphs, Proc. Colloq. Tihany, 1966 – volume: 282 start-page: 113 year: 2004 end-page: 122 ident: b8 article-title: A new Turán-type theorem for cliques in graphs publication-title: Discrete Math. – volume: 120 start-page: 722 year: 2013 end-page: 732 ident: b23 article-title: On the number of pentagons in triangle-free graphs publication-title: J. Combin. Theory Ser. A – volume: 7 start-page: 459 year: 1962 end-page: 474 ident: b10 article-title: On the number of complete subgraphs contained in certain graphs publication-title: M. Tud. Akad. Mat. Kut. Intéz. Közl. – start-page: 399 year: 1978 end-page: 401 ident: b29 article-title: Regular partitions of graphs publication-title: Problèmes Combinatoires et Théorie des Graphes, Proc. Colloque Inter. CNRS – volume: 308 start-page: 4332 year: 2008 end-page: 4336 ident: b5 article-title: Pentagons vs. triangles publication-title: Discrete Math. – volume: 115 start-page: 66 year: 2015 end-page: 71 ident: b14 article-title: A proof of the stability of extremal graphs, Simonovits’ stability from Szemerédi’s regularity publication-title: J. Combin. Theory Ser. B – volume: 9 start-page: 567 year: 2018 end-page: 597 ident: b2 article-title: Many publication-title: J. Comb. – reference: L. Gishboliner, A. Shapira, A generalized Turán problem and its applications, – volume: 3 start-page: 50 year: 1954 end-page: 57 ident: b24 article-title: On a problem of k. zarankiewicz publication-title: Colloq. Math. – volume: 8 start-page: 205 year: 1974 end-page: 218 ident: b4 article-title: On the connection between chromatic number, maximal clique and minimum degree of a graph publication-title: Discrete Math. – volume: 48 start-page: 436 year: 1941 end-page: 452 ident: b30 article-title: On an extremal problem in graph theory publication-title: Mat. Fiz. Lapok – reference: D. Gerbner, A. Methuku, M. Vizer, Generalized Turán problems for disjoint copies of graphs, – volume: 154 start-page: 598 year: 2018 end-page: 609 ident: b27 article-title: Some extremal results on complete degenerate hypergraphs publication-title: J. Combin. Theory, Ser. A – volume: 3 start-page: 181 year: 1983 end-page: 192 ident: b13 article-title: Supersaturated graphs and hypergraphs publication-title: Combinatorica – volume: 7 start-page: 31 year: 1991 end-page: 37 ident: b22 article-title: On the maximal number of certain subgraphs in publication-title: Graphs Combin. – volume: 341 start-page: 1253 year: 2018 end-page: 1263 ident: b15 article-title: Extensions of a theorem of Erdős on nonhamiltonian graphs publication-title: Discrete Math. – reference: . – volume: 27 start-page: 274 year: 2018 end-page: 288 ident: b25 article-title: Induced Turán numbers publication-title: Combin. Probab. Comput. – start-page: 184 year: 2006 end-page: 185 ident: b7 article-title: Graph Theory – volume: 21 start-page: 187 year: 2012 end-page: 191 ident: b21 article-title: The maximum number of triangles in publication-title: Combin. Probab. Comput. – reference: P. Erdős, Some recent results on extremal problems in graph theory, in: Theory of Graphs, International Symp. Rome, 1966, pp. 118–123. – reference: D. Gerbner, B. Keszegh, C. Palmer, B. Patkós, On the number of cycles in a graph with restricted cycle lengths, – volume: 1 start-page: 51 year: 1966 end-page: 57 ident: b12 article-title: A limit theorem in graph theory publication-title: Studia Sci. Math. Hungar. – volume: 102 start-page: 1061 year: 2012 end-page: 1066 ident: b20 article-title: On the maximum number of five-cycles in a triangle-free graph publication-title: J. Combin. Theory Ser. B – volume: 128 start-page: 219 year: 2018 end-page: 226 ident: b26 article-title: The maximum number of cliques in graphs without long cycles publication-title: J. Combin. Theory Ser. B – start-page: 77 year: 1968 end-page: 81 ident: b11 article-title: On some new inequalities concerning extremal properties of graphs publication-title: Theory of Graphs, Proc. Colloq. Tihany, 1966 – ident: 10.1016/j.ejc.2019.103026_b16 – start-page: 399 year: 1978 ident: 10.1016/j.ejc.2019.103026_b29 article-title: Regular partitions of graphs – volume: 3 start-page: 181 year: 1983 ident: 10.1016/j.ejc.2019.103026_b13 article-title: Supersaturated graphs and hypergraphs publication-title: Combinatorica doi: 10.1007/BF02579292 – volume: 108 start-page: 92 year: 2014 ident: 10.1016/j.ejc.2019.103026_b1 article-title: An improved error term for minimal H-decompositions of graphs publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2014.03.001 – ident: 10.1016/j.ejc.2019.103026_b18 – volume: 154 start-page: 598 year: 2018 ident: 10.1016/j.ejc.2019.103026_b27 article-title: Some extremal results on complete degenerate hypergraphs publication-title: J. Combin. Theory, Ser. A doi: 10.1016/j.jcta.2017.10.002 – volume: 102 start-page: 1061 year: 2012 ident: 10.1016/j.ejc.2019.103026_b20 article-title: On the maximum number of five-cycles in a triangle-free graph publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2012.04.001 – volume: 48 start-page: 436 year: 1941 ident: 10.1016/j.ejc.2019.103026_b30 article-title: On an extremal problem in graph theory publication-title: Mat. Fiz. Lapok – volume: 7 start-page: 459 year: 1962 ident: 10.1016/j.ejc.2019.103026_b10 article-title: On the number of complete subgraphs contained in certain graphs publication-title: M. Tud. Akad. Mat. Kut. Intéz. Közl. – volume: 115 start-page: 66 year: 2015 ident: 10.1016/j.ejc.2019.103026_b14 article-title: A proof of the stability of extremal graphs, Simonovits’ stability from Szemerédi’s regularity publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2015.05.001 – volume: 1 start-page: 51 year: 1966 ident: 10.1016/j.ejc.2019.103026_b12 article-title: A limit theorem in graph theory publication-title: Studia Sci. Math. Hungar. – volume: 282 start-page: 113 year: 2004 ident: 10.1016/j.ejc.2019.103026_b8 article-title: A new Turán-type theorem for cliques in graphs publication-title: Discrete Math. doi: 10.1016/j.disc.2003.11.007 – start-page: 279 year: 1968 ident: 10.1016/j.ejc.2019.103026_b28 article-title: A method for solving extremal problems in graph theory, stability problems – volume: 121 start-page: 146 year: 2016 ident: 10.1016/j.ejc.2019.103026_b3 article-title: Many T copies in H-free graphs publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2016.03.004 – volume: 3 start-page: 50 year: 1954 ident: 10.1016/j.ejc.2019.103026_b24 article-title: On a problem of k. zarankiewicz publication-title: Colloq. Math. doi: 10.4064/cm-3-1-50-57 – ident: 10.1016/j.ejc.2019.103026_b17 – ident: 10.1016/j.ejc.2019.103026_b19 – start-page: 184 year: 2006 ident: 10.1016/j.ejc.2019.103026_b7 – volume: 120 start-page: 722 issue: 3 year: 2013 ident: 10.1016/j.ejc.2019.103026_b23 article-title: On the number of pentagons in triangle-free graphs publication-title: J. Combin. Theory Ser. A doi: 10.1016/j.jcta.2012.12.008 – volume: 27 start-page: 274 year: 2018 ident: 10.1016/j.ejc.2019.103026_b25 article-title: Induced Turán numbers publication-title: Combin. Probab. Comput. doi: 10.1017/S0963548317000542 – volume: 341 start-page: 1253 year: 2018 ident: 10.1016/j.ejc.2019.103026_b15 article-title: Extensions of a theorem of Erdős on nonhamiltonian graphs publication-title: Discrete Math. doi: 10.1016/j.disc.2017.12.018 – volume: 8 start-page: 205 year: 1974 ident: 10.1016/j.ejc.2019.103026_b4 article-title: On the connection between chromatic number, maximal clique and minimum degree of a graph publication-title: Discrete Math. doi: 10.1016/0012-365X(74)90133-2 – volume: 18 start-page: 629 issue: 6 year: 1994 ident: 10.1016/j.ejc.2019.103026_b6 article-title: The inducibility of complete bipartite graphs publication-title: J. Graph Theory doi: 10.1002/jgt.3190180610 – volume: 21 start-page: 187 issue: 1–2 year: 2012 ident: 10.1016/j.ejc.2019.103026_b21 article-title: The maximum number of triangles in C2k+1-free graphs publication-title: Combin. Probab. Comput. doi: 10.1017/S0963548311000629 – volume: 7 start-page: 31 year: 1991 ident: 10.1016/j.ejc.2019.103026_b22 article-title: On the maximal number of certain subgraphs in Kr-free graphs publication-title: Graphs Combin. doi: 10.1007/BF01789461 – volume: 128 start-page: 219 year: 2018 ident: 10.1016/j.ejc.2019.103026_b26 article-title: The maximum number of cliques in graphs without long cycles publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2017.08.005 – ident: 10.1016/j.ejc.2019.103026_b9 – start-page: 77 year: 1968 ident: 10.1016/j.ejc.2019.103026_b11 article-title: On some new inequalities concerning extremal properties of graphs – volume: 308 start-page: 4332 year: 2008 ident: 10.1016/j.ejc.2019.103026_b5 article-title: Pentagons vs. triangles publication-title: Discrete Math. doi: 10.1016/j.disc.2007.08.016 – volume: 9 start-page: 567 year: 2018 ident: 10.1016/j.ejc.2019.103026_b2 article-title: Many T copies in H-free subgraphs of random graphs publication-title: J. Comb. |
| SSID | ssj0011533 |
| Score | 2.470316 |
| Snippet | For graphs T,H, let ex(n,T,H) denote the maximum number of copies of T in an n-vertex H-free graph. In this paper we prove some sharp results on this... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 103026 |
| Title | Some sharp results on the generalized Turán numbers |
| URI | https://dx.doi.org/10.1016/j.ejc.2019.103026 |
| Volume | 84 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELZKu8CAeIryqDwwIYXGiRPHY6moClU70FZ0i_wKtCpp1aQLA_-F38Ifw86jAgkYmCJZPin-bN1Dd_cdAJc4sLWR4rZFFMEWRlxZVCHXiqhkwiTigizR3h_43TG-n3iTCmiXvTCmrLLQ_blOz7R1sdIs0Gwup9PmMGt186k2aa7Jn-oQqOa41PeqoNa663UHm2SCcWnKsYRGoExuZmVeamaIDBE13ecZxcJP5umLyensgd3CV4St_Hf2QUXFB2CnvyFaTQ4BHi5eFEye2WoJdeC8nqcJXMRQ74BPOaH09FVJOFqvPt5jmI__SI7AuHM7anetYhCCJRxKUktgTAniCDHmc0KlQxzuCE_ZMuBECkZ8ipXEtqu4Pp4rBY-YQF7EMcMMaQ1yDKrxIlYnAHKuGHKUiAiSmAf6CqPAo8yVSoNAGKkDuzx_KAqWcDOsYh6W5WCzUEMWGsjCHLI6uNqILHOKjL824xLU8Ns9h1qF_y52-j-xM7DtmPg4q7I-B9V0tVYX2olIeQNsXb-hRvFUzLf38NjTq3eTm0-k3cgX |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELWqcgAOiFWU1QdOSFHjxInjI1RULbS9tJV6s7wFWpW0atILf8O38GPYWSqQgAPXaEaKn61ZNDNvALjBkWuclHAdogl2MBLaoRr5TkwVl7YQF-WF9v4g7Izx4ySY1ECrmoWxbZWl7S9sem6tyy_NEs3mcjptDvNRt5Aal-bb-qlJgbZMNBBaAv3u5H5TSrABTbWU0IpXpc28yUvPLI0honb2PCdY-Mk5fXE47X2wV0aK8K74mQNQ08kh2O1vaFbTI4CHi1cN0xe-WkKTNq_nWQoXCTQS8Lmgk56-aQVH69XHewKL5R_pMRi3H0atjlOuQXCkR0nmSIwpQQIhzkNBqPKIJzwZaFdFgijJSUixVtj1tTDH85UUMZcoiAXmmCNjP05APVkk-hRAITRHnpYxQQqLyFxgHAWU-0obEAgnDeBW52ey5Ai3qyrmrGoGmzEDGbOQsQKyBrjdqCwLgoy_hHEFKvt2y8wY8N_Vzv6ndg22O6N-j_W6g6dzsOPZTDnvt74A9Wy11pcmnMjEVf5cPgF61sZI |
| 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=Some+sharp+results+on+the+generalized+Tur%C3%A1n+numbers&rft.jtitle=European+journal+of+combinatorics&rft.au=Ma%2C+Jie&rft.au=Qiu%2C+Yu&rft.date=2020-02-01&rft.pub=Elsevier+Ltd&rft.issn=0195-6698&rft.eissn=1095-9971&rft.volume=84&rft_id=info:doi/10.1016%2Fj.ejc.2019.103026&rft.externalDocID=S0195669819301271 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0195-6698&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0195-6698&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0195-6698&client=summon |