{"publication":"Proceedings of the American Mathematical Society","status":"public","acknowledgement":"This research was supported by the Swiss National Science Foundation (SNF Projects 200021-125309 and 200020-138230","volume":144,"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1404.2106","open_access":"1"}],"issue":"4","publication_status":"published","author":[{"first_name":"Anna","last_name":"Gundert","full_name":"Gundert, Anna"},{"full_name":"Wagner, Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"title":"On topological minors in random simplicial complexes","abstract":[{"text":"For random graphs, the containment problem considers the probability that a binomial random graph G(n, p) contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well known that the (sharp) threshold is at p = 1/n. We consider a natural analogue of this question for higher-dimensional random complexes Xk(n, p), first studied by Cohen, Costa, Farber and Kappeler for k = 2. Improving previous results, we show that p = Θ(1/ √n) is the (coarse) threshold for containing a subdivision of any fixed complete 2-complex. For higher dimensions k &gt; 2, we get that p = O(n−1/k) is an upper bound for the threshold probability of containing a subdivision of a fixed k-dimensional complex.","lang":"eng"}],"citation":{"ama":"Gundert A, Wagner U. On topological minors in random simplicial complexes. <i>Proceedings of the American Mathematical Society</i>. 2016;144(4):1815-1828. doi:<a href=\"https://doi.org/10.1090/proc/12824\">10.1090/proc/12824</a>","apa":"Gundert, A., &#38; Wagner, U. (2016). On topological minors in random simplicial complexes. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/12824\">https://doi.org/10.1090/proc/12824</a>","ista":"Gundert A, Wagner U. 2016. On topological minors in random simplicial complexes. Proceedings of the American Mathematical Society. 144(4), 1815–1828.","ieee":"A. Gundert and U. Wagner, “On topological minors in random simplicial complexes,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4. American Mathematical Society, pp. 1815–1828, 2016.","chicago":"Gundert, Anna, and Uli Wagner. “On Topological Minors in Random Simplicial Complexes.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/12824\">https://doi.org/10.1090/proc/12824</a>.","mla":"Gundert, Anna, and Uli Wagner. “On Topological Minors in Random Simplicial Complexes.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1815–28, doi:<a href=\"https://doi.org/10.1090/proc/12824\">10.1090/proc/12824</a>.","short":"A. Gundert, U. Wagner, Proceedings of the American Mathematical Society 144 (2016) 1815–1828."},"publisher":"American Mathematical Society","_id":"1523","page":"1815 - 1828","year":"2016","type":"journal_article","day":"01","oa_version":"Preprint","date_updated":"2021-01-12T06:51:22Z","quality_controlled":"1","scopus_import":1,"month":"04","intvolume":"       144","date_published":"2016-04-01T00:00:00Z","date_created":"2018-12-11T11:52:30Z","publist_id":"5650","doi":"10.1090/proc/12824"}