Geodesic
Independence Numbers of Random Subgraphs of a~Distance Graph
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 288-297

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We consider the so-called distance graph $G(n,3,1)$, whose vertices can be identified with three-element subsets of the set $\{1,2,\dots,n\}$, two vertices being joined by an edge if and only if the corresponding subsets have exactly one common element. We study some properties of random subgraphs of $G(n,3,1)$ in the Erdős–Rényi model, in which each edge is included in the subgraph with some given probability $p$ independently of the other edges. We find the asymptotics of the independence number of a random subgraph of $G(n,3,1)$.
Keywords: distance graph, random subgraph, independence number, Erdős–Rényi model. 
@article{MZM_2016_99_2_a11,
     author = {M. M. Pyaderkin},
     title = {Independence {Numbers} of {Random} {Subgraphs} of {a~Distance} {Graph}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {288--297},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a11/}
}
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M. M. Pyaderkin. Independence Numbers of Random Subgraphs of a~Distance Graph. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 288-297. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a11/