In a recent paper, J. Gaudio and E. Mossel studied the shotgun assembly of the Erdős-Rényi graph $\mathcal G(n,p_n)$ with $p_n=n^{-\alpha}$, and showed that the graph is reconstructable form its $1$-neighbourhoods if $0<\alpha < 1/3$ and not reconstructable from its $1$-neighbourhoods if $1/2 <\alpha<1$. In this article, we generalise the notion of reconstruction of graphs to the reconstruction of simplicial complexes. We show that the Linial-Meshulam model $Y_{d}(n,p_n)$ on $n$ vertices with $p_n=n^{-\alpha}$ is reconstructable from its $1$-neighbourhoods when $0< \alpha < 1/3$ and is not reconstructable form its $1$-neighbourhoods when $1/2 < \alpha < 1$.
@article{10_37236_12588,
author = {Kartick Adhikari and Sukrit Chakraborty},
title = {Shotgun assembly of {Linial-Meshulam} model},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/12588},
zbl = {8097669},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12588/}
}
TY - JOUR
AU - Kartick Adhikari
AU - Sukrit Chakraborty
TI - Shotgun assembly of Linial-Meshulam model
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12588/
DO - 10.37236/12588
ID - 10_37236_12588
ER -
%0 Journal Article
%A Kartick Adhikari
%A Sukrit Chakraborty
%T Shotgun assembly of Linial-Meshulam model
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12588/
%R 10.37236/12588
%F 10_37236_12588
Kartick Adhikari; Sukrit Chakraborty. Shotgun assembly of Linial-Meshulam model. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12588
