{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T03:38:15Z","timestamp":1752982695978,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["639.032.529","612.001.409"],"award-info":[{"award-number":["639.032.529","612.001.409"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-16-CE40-0009-01"],"award-info":[{"award-number":["ANR-16-CE40-0009-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"LabEx PERSYVAL-Lab","award":["ANR-11-LABX- 0025"],"award-info":[{"award-number":["ANR-11-LABX- 0025"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s00454-022-00378-9","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:05:32Z","timestamp":1648519532000},"page":"1139-1156","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Contractibility of Random Vietoris\u2013Rips Complexes"],"prefix":"10.1007","volume":"69","author":[{"given":"Tobias","family":"M\u00fcller","sequence":"first","affiliation":[]},{"given":"Mat\u011bj","family":"Stehl\u00edk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"issue":"4","key":"378_CR1","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1007\/s00454-014-9621-6","volume":"52","author":"RJ Adler","year":"2014","unstructured":"Adler, R.J., Bobrowski, O., Weinberger, Sh.: Crackle: the homology of noise. Discrete Comput. Geom. 52(4), 680\u2013704 (2014)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"378_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0166-218X(84)90073-8","volume":"8","author":"M Aigner","year":"1984","unstructured":"Aigner, M., Fromme, M.: A game of cops and robbers. Discrete Appl. Math. 8(1), 1\u201311 (1984)","journal-title":"Discrete Appl. Math."},{"key":"378_CR3","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.dam.2014.06.004","volume":"178","author":"N Alon","year":"2014","unstructured":"Alon, N., Pra\u0142at, P.: Chasing robbers on random geometric graphs\u2014an alternative approach. Discrete Appl. Math. 178, 149\u2013152 (2014)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"378_CR4","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1214\/10-AAP718","volume":"21","author":"J Balogh","year":"2011","unstructured":"Balogh, J., Bollob\u00e1s, B., Krivelevich, M., M\u00fcller, T., Walters, M.: Hamilton cycles in random geometric graphs. Ann. Appl. Probab. 21(3), 1053\u20131072 (2011)","journal-title":"Ann. Appl. Probab."},{"issue":"6","key":"378_CR5","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1017\/S0963548312000338","volume":"21","author":"A Beveridge","year":"2012","unstructured":"Beveridge, A., Dudek, A., Frieze, A., M\u00fcller, T.: Cops and robbers on geometric graphs. Comb. Probab. Comput. 21(6), 816\u2013834 (2012)","journal-title":"Comb. Probab. Comput."},{"key":"378_CR6","unstructured":"Bj\u00f6rner, A.: Topological methods. In: Handbook of Combinatorics, vol.\u00a02, pp. 1819\u20131872. Elsevier, Amsterdam (1995)"},{"key":"378_CR7","unstructured":"Bobrowski, O.: Homological connectivity in random \u010cech complexes (2019). arXiv:1906.04861"},{"issue":"3\u20134","key":"378_CR8","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s41468-017-0010-0","volume":"1","author":"O Bobrowski","year":"2018","unstructured":"Bobrowski, O., Kahle, M.: Topology of random geometric complexes: a survey. J. Appl. Comput. Topol. 1(3\u20134), 331\u2013364 (2018)","journal-title":"J. Appl. Comput. Topol."},{"issue":"1","key":"378_CR9","doi-asserted-by":"publisher","first-page":"288","DOI":"10.3150\/15-BEJ744","volume":"23","author":"O Bobrowski","year":"2017","unstructured":"Bobrowski, O., Mukherjee, S., Taylor, J.E.: Topological consistency via kernel estimation. Bernoulli 23(1), 288\u2013328 (2017)","journal-title":"Bernoulli"},{"issue":"3","key":"378_CR10","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1002\/rsa.20800","volume":"54","author":"O Bobrowski","year":"2019","unstructured":"Bobrowski, O., Oliveira, G.: Random \u010cech complexes on Riemannian manifolds. Random Struct. Algorithms 54(3), 373\u2013412 (2019)","journal-title":"Random Struct. Algorithms"},{"issue":"3","key":"378_CR11","doi-asserted-by":"publisher","first-page":"1869","DOI":"10.1214\/19-AIHP1020","volume":"56","author":"SK Iyer","year":"2020","unstructured":"Iyer, S.K., Yogeshwaran, D.: Thresholds for vanishing of \u2018isolated\u2019 faces in random \u010cech and Vietoris\u2013Rips complexes. Ann. Inst. Henri Poincar\u00e9 Probab. Stat. 56(3), 1869\u20131897 (2020)","journal-title":"Ann. Inst. Henri Poincar\u00e9 Probab. Stat."},{"issue":"6","key":"378_CR12","doi-asserted-by":"publisher","first-page":"1658","DOI":"10.1016\/j.disc.2008.02.037","volume":"309","author":"M Kahle","year":"2009","unstructured":"Kahle, M.: Topology of random clique complexes. Discrete Math. 309(6), 1658\u20131671 (2009)","journal-title":"Discrete Math."},{"issue":"3","key":"378_CR13","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00454-010-9319-3","volume":"45","author":"M Kahle","year":"2011","unstructured":"Kahle, M.: Random geometric complexes. Discrete Comput. Geom. 45(3), 553\u2013573 (2011)","journal-title":"Discrete Comput. Geom."},{"issue":"3","key":"378_CR14","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.4007\/annals.2014.179.3.5","volume":"179","author":"M Kahle","year":"2014","unstructured":"Kahle, M.: Sharp vanishing thresholds for cohomology of random flag complexes. Ann. Math. 179(3), 1085\u20131107 (2014)","journal-title":"Ann. Math."},{"key":"378_CR15","doi-asserted-by":"crossref","unstructured":"de\u00a0Kergorlay, H.-L., Tillmann, U., Vipond, O.: Random \u010cech complexes on manifolds with boundary. Random Struct. Algorithms (2022). https:\/\/onlinelibrary.wiley.com\/doi\/full\/10.1002\/rsa.21062","DOI":"10.1002\/rsa.21062"},{"key":"378_CR16","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71962-5","volume-title":"Combinatorial Algebraic Topology","author":"D Kozlov","year":"2008","unstructured":"Kozlov, D.: Combinatorial Algebraic Topology. Algorithms and Computation in Mathematics, vol. 21. Springer, Berlin (2008)"},{"issue":"4","key":"378_CR17","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s00493-006-0027-9","volume":"26","author":"N Linial","year":"2006","unstructured":"Linial, N., Meshulam, R.: Homological connectivity of random $$2$$-complexes. Combinatorica 26(4), 475\u2013487 (2006)","journal-title":"Combinatorica"},{"key":"378_CR18","unstructured":"Malen, G.: Collapsibility of random clique complexes (2019). arXiv:1903.05055"},{"issue":"3","key":"378_CR19","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1002\/rsa.20238","volume":"34","author":"R Meshulam","year":"2009","unstructured":"Meshulam, R., Wallach, N.: Homological connectivity of random $$k$$-dimensional complexes. Random Struct. Algorithms 34(3), 408\u2013417 (2009)","journal-title":"Random Struct. Algorithms"},{"key":"378_CR20","series-title":"Annals of Mathematics Studies","volume-title":"Elementary Differential Topology","author":"JR Munkres","year":"1966","unstructured":"Munkres, J.R.: Elementary Differential Topology. Annals of Mathematics Studies, vol. 54. Princeton University Press, Princeton (1966)"},{"issue":"1\u20133","key":"378_CR21","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s00454-008-9053-2","volume":"39","author":"P Niyogi","year":"2008","unstructured":"Niyogi, P., Smale, S., Weinberger, Sh.: Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39(1\u20133), 419\u2013441 (2008)","journal-title":"Discrete Comput. Geom."},{"issue":"3","key":"378_CR22","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1137\/090762932","volume":"40","author":"P Niyogi","year":"2011","unstructured":"Niyogi, P., Smale, S., Weinberger, Sh.: A topological view of unsupervised learning from noisy data. SIAM J. Comput. 40(3), 646\u2013663 (2011)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"378_CR23","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1214\/aoap\/1034625335","volume":"7","author":"MD Penrose","year":"1997","unstructured":"Penrose, M.D.: The longest edge of the random minimal spanning tree. Ann. Appl. Probab. 7(2), 340\u2013361 (1997)","journal-title":"Ann. Appl. Probab."},{"issue":"2","key":"378_CR24","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/(SICI)1098-2418(199909)15:2<145::AID-RSA2>3.0.CO;2-G","volume":"15","author":"MD Penrose","year":"1999","unstructured":"Penrose, M.D.: On $$k$$-connectivity for a geometric random graph. Random Struct. Algorithms 15(2), 145\u2013164 (1999)","journal-title":"Random Struct. Algorithms"},{"key":"378_CR25","unstructured":"Quilliot, A.: Jeux et Pointes Fixes sur les Graphes. PhD thesis, Universit\u00e9 de Paris VI (1978)"},{"key":"378_CR26","unstructured":"Rudin, W.: Principles of Mathematical Analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, New York (1976)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-022-00378-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-022-00378-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-022-00378-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T05:29:12Z","timestamp":1683782952000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-022-00378-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,28]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["378"],"URL":"https:\/\/doi.org\/10.1007\/s00454-022-00378-9","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2022,3,28]]},"assertion":[{"value":"8 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}