Geodesic
Independence numbers of random sparse hypergraphs
Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 126-144

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The paper is concerned with the asymptotic behaviour of the independence number for the binomial model of a random $k$-regular hypergraph $H(n,k,p)$ in a sparse case, when $p=c/{n-1\choose k-1}$ with positive constant $c>0$. The independence number $\alpha(H(n,k,p))$ is shown to satisfy the law of large numbers $$ \frac{\alpha(H(n,k,p))}{n}\stackrel{P}{\to}\gamma(c)\;\; as n\to+\infty $$ with some constant $\gamma(c)>0$. We also shows that $\gamma(c)>0$ is a solution of some transcendental equation for small values of $c\leqslant (k-1)^{-1}$.
Keywords: hypergraph, independence number, sparse hypergraphs, the method of interpolation, the Karp–Sipser algorithm. 
@article{DM_2016_28_3_a8,
     author = {A. S. Semenov and D. A. Shabanov},
     title = {Independence numbers of random sparse hypergraphs},
     journal = {Diskretnaya Matematika},
     pages = {126--144},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_3_a8/}
}
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A. S. Semenov; D. A. Shabanov. Independence numbers of random sparse hypergraphs. Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 126-144. http://geodesic.mathdoc.fr/item/DM_2016_28_3_a8/