Homological connectivity of random hypergraphs
| Autor: | Cooley, Oliver, Haxell, Penny, Kang, Mihyun, Sprüssel, Philipp |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first homology groups with coefficients in $\mathbb{F}_2$ vanish. Although this is not intrinsically a monotone property, we show that it nevertheless has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction. Comment: 21 pages |
| Databáze: | arXiv |
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