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arXiv · 1604.00842

Homological connectivity of random hypergraphs

Oliver Cooley·Penny Haxell·Mihyun Kang·Philipp Sprüssel
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Abstract

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.

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Oliver Cooley, Penny Haxell, Mihyun Kang, Philipp Sprüssel. 2016-04-04. Homological connectivity of random hypergraphs. https://arxiv.org/abs/1604.00842

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