{"acknowledgement":"This research was supported by the Swiss National Science Foundation (SNF Projects 200021-125309 and 200020-138230","year":"2016","publist_id":"5650","volume":144,"intvolume":"       144","language":[{"iso":"eng"}],"_id":"1523","citation":{"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>.","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.","ista":"Gundert A, Wagner U. 2016. On topological minors in random simplicial complexes. Proceedings of the American Mathematical Society. 144(4), 1815–1828.","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>","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>.","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>","short":"A. Gundert, U. Wagner, Proceedings of the American Mathematical Society 144 (2016) 1815–1828."},"page":"1815 - 1828","doi":"10.1090/proc/12824","publication":"Proceedings of the American Mathematical Society","author":[{"full_name":"Gundert, Anna","last_name":"Gundert","first_name":"Anna"},{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"status":"public","title":"On topological minors in random simplicial complexes","quality_controlled":"1","scopus_import":1,"publisher":"American Mathematical Society","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:52:30Z","oa":1,"oa_version":"Preprint","main_file_link":[{"url":"http://arxiv.org/abs/1404.2106","open_access":"1"}],"abstract":[{"lang":"eng","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."}],"department":[{"_id":"UlWa"}],"issue":"4","publication_status":"published","date_published":"2016-04-01T00:00:00Z","date_updated":"2021-01-12T06:51:22Z","month":"04","day":"01","type":"journal_article"}