Universität zu Köln

Gundert, Anna and Wagner, Uli ORCID: 0000-0002-1494-0568 (2016). ON TOPOLOGICAL MINORS IN RANDOM SIMPLICIAL COMPLEXES. Proc. Amer. Math. Soc., 144 (4). S. 1815 - 1829. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6826

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Abstract

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 X-k(n, p), first studied by Cohen, Costa, Farber and Kappeler for k = 2. Improving previous results, we show that p = Theta(1/root n) is the (coarse) threshold for containing a subdivision of any fixed complete 2-complex. For higher dimensions k > 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gundert, Anna UNSPECIFIED UNSPECIFIED UNSPECIFIED Wagner, Uli UNSPECIFIED orcid.org/0000-0002-1494-0568 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-280936
DOI:	10.1090/proc/12824
Journal or Publication Title:	Proc. Amer. Math. Soc.
Volume:	144
Number:	4
Page Range:	S. 1815 - 1829
Date:	2016
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6826
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HOMOLOGICAL CONNECTIVITY; TOP HOMOLOGY; MAPS; ENUMERATION; NUMBER Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28093