A Hamiltonian cycle in a graph is a spanning subgraph that is homeomorphic to a circle. With this in mind, it is natural to define a Hamiltonian d-sphere in a d-dimensional simplicial complex as a spanning subcomplex that is homeomorphic to a d-dimensional sphere. We consider the Linial-Meshulam model for random simplicial complexes, and prove that there is a sharp threshold at p=e/gamma n for the appearance of a Hamiltonian 2-sphere in a random 2-complex, where gamma=44/33.
Journal article
A sharp threshold for spanning 2-spheres in random 2-complexes
Proceedings of the London Mathematical Society, Vol.119(3), pp.733-780
Sep/2019
Abstract
Details
- Title
- A sharp threshold for spanning 2-spheres in random 2-complexes
- Creators
- Zur Luria (Corresponding Author) - Jerusalem Coll EngnRan J. Tessler (null) - The Weizmann Institute of Science
- Resource Type
- Journal article
- Publication Details
- Proceedings of the London Mathematical Society, Vol.119(3), pp.733-780; Sep/2019
- Number of pages
- 48
- Language
- English
- DOI
- https://doi.org/10.1112/plms.12247
- Grant note
- Z. L. was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. R. T., Incumbent of the Lilian and George Lyttle Career Development Chair, was supported by a research grant from the Center for New Scientists of Weizmann Institute, and by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.
- Record Identifier
- 993263241203596
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