Homological connectedness of random hypergraphs

Oliver Josef Nikolaus Cooley; Penny Haxell; Mihyun Kang; Philipp Sprüssel

doi:10.1016/j.endm.2017.06.049

Homological connectedness of random hypergraphs

Oliver Josef Nikolaus Cooley, Penny Haxell, Mihyun Kang, Philipp Sprüssel

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Conference article › peer-review

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 first homology group with coefficients in F2 vanishes and the zero-th homology group is isomorphic to F2. Although this is not intrinsically a monotone property, we show that it has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.

Original language	English
Pages (from-to)	279-285
Journal	Electronic Notes in Discrete Mathematics
Volume	61
DOIs	https://doi.org/10.1016/j.endm.2017.06.049
Publication status	Published - 2017
Event	European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2017), TU Wien: Eurocomb 2017 - TU Wien, Wien, Austria Duration: 28 Aug 2017 → 1 Sept 2017

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10.1016/j.endm.2017.06.049

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title = "Homological connectedness of random hypergraphs",

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 first homology group with coefficients in F2 vanishes and the zero-th homology group is isomorphic to F2. Although this is not intrinsically a monotone property, we show that it has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.",

author = "Cooley, {Oliver Josef Nikolaus} and Penny Haxell and Mihyun Kang and Philipp Spr{\"u}ssel",

year = "2017",

doi = "10.1016/j.endm.2017.06.049",

language = "English",

volume = "61",

pages = "279--285",

journal = "Electronic Notes in Discrete Mathematics ",

issn = "1571-0653",

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T1 - Homological connectedness of random hypergraphs

AU - Cooley, Oliver Josef Nikolaus

AU - Haxell, Penny

AU - Kang, Mihyun

AU - Sprüssel, Philipp

PY - 2017

Y1 - 2017

N2 - 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 first homology group with coefficients in F2 vanishes and the zero-th homology group is isomorphic to F2. Although this is not intrinsically a monotone property, we show that it has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.

AB - 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 first homology group with coefficients in F2 vanishes and the zero-th homology group is isomorphic to F2. Although this is not intrinsically a monotone property, we show that it 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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U2 - 10.1016/j.endm.2017.06.049

DO - 10.1016/j.endm.2017.06.049

M3 - Conference article

SN - 1571-0653

VL - 61

SP - 279

EP - 285

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

T2 - European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2017), TU Wien

Y2 - 28 August 2017 through 1 September 2017

ER -

Homological connectedness of random hypergraphs

Abstract

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