{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T08:17:09Z","timestamp":1774513029659,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,11,20]],"date-time":"2021-11-20T00:00:00Z","timestamp":1637366400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,20]],"date-time":"2021-11-20T00:00:00Z","timestamp":1637366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s00493-021-4530-9","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T06:02:42Z","timestamp":1637560962000},"page":"803-813","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Bounded VC-Dimension Implies the Schur-Erd\u0151s Conjecture"],"prefix":"10.1007","volume":"41","author":[{"given":"Jacob","family":"Fox","sequence":"first","affiliation":[]},{"given":"J\u00e1nos","family":"Pach","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Suk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,20]]},"reference":[{"key":"4530_CR1","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.jcta.2004.12.008","volume":"111","author":"N Alon","year":"2005","unstructured":"N. Alon, J. Pach, R. Pinchasi, R. Radoi\u010dI\u0107 and M. Sharir: Crossing patterns of semi-algebraic sets, J. Combin. Theory, Ser. A 111 (2005), 310\u2013326.","journal-title":"J. Combin. Theory, Ser. A"},{"key":"4530_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0304-3975(91)90261-Y","volume":"84","author":"B Chazelle","year":"1991","unstructured":"B. Chazelle, H. Edelsbrunner, L. Guibas and M. Sharir: A singly exponential stratification scheme for real semi-algebraic varieties and its applications, Theor. Comput. Sci. 84 (1991), 77\u2013105.","journal-title":"Theor. Comput. Sci."},{"key":"4530_CR3","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0012-365X(73)90125-8","volume":"5","author":"F Chung","year":"1973","unstructured":"F. Chung: On the Ramsey numbers N(3,3,\u2026,3;2), Discrete Math. 5 (1973), 317\u2013321.","journal-title":"Discrete Math."},{"key":"4530_CR4","doi-asserted-by":"crossref","unstructured":"F. Chung and R. Graham: Erd\u0151s on Graphs: His Legacy of Unsolved Problems, AK Peters\/CRC Press, 1998.","DOI":"10.1201\/9781439863879"},{"key":"4530_CR5","first-page":"74","volume":"2","author":"P Erd\u0151s","year":"1938","unstructured":"P. Erd\u0151s: On sequences of integers no one of which divides the product of two others and on some related problems, Inst. Math. Mech. Univ. Tomsk 2 (1938), 74\u201382.","journal-title":"Inst. Math. Mech. Univ. Tomsk"},{"key":"4530_CR6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/0166-218X(89)90045-0","volume":"25","author":"P Erd\u0151s","year":"1989","unstructured":"P. Erd\u0151s and A. Hajnal: Ramsey-type theorems, Discrete Appl. Math. 25 (1989), 37\u201352.","journal-title":"Discrete Appl. Math."},{"key":"4530_CR7","first-page":"49","volume":"671","author":"J Fox","year":"2012","unstructured":"J. Fox, M. Gromov, V. Lafforgue, A. Naor and J. Pach: Overlap properties of geometric transversals, Reine Angew. Math. (Crelle\u2019s Journal) 671 (2012), 49\u201383.","journal-title":"Reine Angew. Math. (Crelle\u2019s Journal)"},{"key":"4530_CR8","doi-asserted-by":"publisher","first-page":"1785","DOI":"10.4171\/JEMS\/705","volume":"19","author":"J Fox","year":"2017","unstructured":"J. Fox, J. Pach, A. Sheffer, A. Suk and J. Zahl: A semi-algebraic version of Zarankiewicz\u2019s problem, J. Eur. Math. Soc. (JEMS) 19 (2017), 1785\u20131810.","journal-title":"J. Eur. Math. Soc. (JEMS)"},{"key":"4530_CR9","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1007\/s00454-018-0046-5","volume":"61","author":"J Fox","year":"2019","unstructured":"J. Fox, J. Pach and A. Suk: Erd\u0151s-Hajnal conjecture for graphs with bounded VC-dimension, Discrete Comput Geom 61 (2019), 809\u2013829.","journal-title":"Discrete Comput Geom"},{"key":"4530_CR10","unstructured":"J. Fox, J. Pach and A. Suk: The Schur-Erd\u0151s problem for semi-algebraic colorings, Israel J. Mathematics, accepted."},{"key":"4530_CR11","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1137\/15M1007355","volume":"45","author":"J Fox","year":"2016","unstructured":"J. Fox, J. Pach and A. Suk: A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing, SIAM J. Computing 45 (2016), 2199\u20132223.","journal-title":"SIAM J. Computing"},{"key":"4530_CR12","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/064","volume-title":"Polynomial Methods in Combinatorics. University Lecture Series","author":"L Guth","year":"2016","unstructured":"L. Guth: Polynomial Methods in Combinatorics. University Lecture Series 64, Amer. Math. Soc., Providence, RI, 2016."},{"key":"4530_CR13","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0097-3165(95)90052-7","volume":"69","author":"D Haussler","year":"1995","unstructured":"D. Haussler: Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension, J. Combin. Theory Ser. A 69 (1995), 217\u2013232.","journal-title":"J. Combin. Theory Ser. A"},{"key":"4530_CR14","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/BF02187876","volume":"2","author":"D Haussler","year":"1987","unstructured":"D. Haussler and E. Welzl: \u03b5-nets and simplex range queries, Discrete Comput. Geom. 2 (1987), 127\u2013151.","journal-title":"Discrete Comput. Geom."},{"key":"4530_CR15","doi-asserted-by":"publisher","first-page":"50","DOI":"10.4064\/cm-3-1-50-57","volume":"3","author":"P K\u0151v\u00e1ri","year":"1954","unstructured":"P. K\u0151v\u00e1ri, V. S\u00f3s and P. Tur\u00e1n: On a problem of Zarankiewicz, Colloq. Math. 3 (1954), 50\u201357.","journal-title":"Colloq. Math."},{"key":"4530_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0039-7","volume-title":"Lectures on Discrete Geometry","author":"J Matou\u0161ek","year":"2002","unstructured":"J. Matou\u0161ek: Lectures on Discrete Geometry, Springer-Verlag, New York, 2002."},{"key":"4530_CR17","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1090\/S0002-9939-1964-0161339-9","volume":"15","author":"J Milnor","year":"1964","unstructured":"J. Milnor: On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964), 275\u2013280.","journal-title":"Proc. Amer. Math. Soc."},{"key":"4530_CR18","first-page":"389","volume":"13","author":"I G Petrovski\u012d","year":"1949","unstructured":"I. G. Petrovski\u012d and O. A. Ole\u012dnik: On the topology of real algebraic surfaces (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 389\u2013402.","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"4530_CR19","first-page":"114","volume":"25","author":"I Schur","year":"1916","unstructured":"I. Schur: \u00dcber die Kongruenz xm + ym = zm (mod p), Jber. Deutsch. Math. Verein. 25 (1916), 114\u2013116.","journal-title":"Jber. Deutsch. Math. Verein."},{"key":"4530_CR20","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/BF02579194","volume":"3","author":"E Szemer\u00e9di","year":"1983","unstructured":"E. Szemer\u00e9di and W. T. Trotter: Extremal problems in discrete geometry, Combinatorica 3 (1983), 381\u2013392.","journal-title":"Combinatorica"},{"key":"4530_CR21","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/1116025","volume":"16","author":"V Vapnik","year":"1971","unstructured":"V. Vapnik and A. Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl. 16 (1971), 264\u2013280.","journal-title":"Theory Probab. Appl."},{"key":"4530_CR22","doi-asserted-by":"crossref","unstructured":"X. Xiaodong, X. Zheng, G. Exoo and S. P. Radziszowski: Constructive lower bounds on classical multicolor Ramsey numbers, Electron. J. Combin. 11 (2004), Research Paper 35.","DOI":"10.37236\/1788"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4530-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-021-4530-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-021-4530-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,31]],"date-time":"2021-12-31T00:03:39Z","timestamp":1640909019000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-021-4530-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,20]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["4530"],"URL":"https:\/\/doi.org\/10.1007\/s00493-021-4530-9","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,20]]},"assertion":[{"value":"26 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 January 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}