Geodesic
The size of the giant component in random hypergraphs: a short proof
Oliver Cooley1 ; Mihyun Kang1 ; Christoph Koch2
1Graz University of Technology
2University of Oxford
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\ge 2$ and $1\le j \le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least $j$ vertices.We prove that certain collections of $j$-sets constructed during a breadth-first search process on $j$-components in a random $k$-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant $j$-component shortly after it appears.
DOI : 10.37236/7712
Classification : 05C65, 05C80
Mots-clés : connected components in \(k\)-uniform hypergraphs

Oliver Cooley  1   ; Mihyun Kang  1   ; Christoph Koch  2

1 Graz University of Technology
2 University of Oxford 
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Oliver Cooley; Mihyun Kang; Christoph Koch. The size of the giant component in random hypergraphs: a short proof. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/7712

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