Geodesic
Modular statistics for subgraph counts in sparse random graphs
Bobby DeMarco ; Jeff Kahn1 ; Amanda Redlich2
1Rutgers University
2Bowdoin College
The electronic journal of combinatorics, Tome 22 (2015) no. 1
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Answering a question of Kolaitis and Kopparty, we show that, for given integer $q>1$ and pairwise nonisomorphic connected graphs $G_1,\dots, G_k$, if $p=p(n) $ is such that $\Pr(G_{n,p}\supseteq G_i)\rightarrow 1$ $\forall i$, then, with $\xi_i$ the number of copies of $G_i$ in $G_{n,p}$, $(\xi_1,\dots, \xi_k)$ is asymptotically uniformly distributed on ${\bf Z}_q^k$.
DOI : 10.37236/4094
Classification : 05C80, 05C42, 03C13
Mots-clés : random graphs, threshold, zero-one law

Bobby DeMarco    ; Jeff Kahn  1   ; Amanda Redlich  2

1 Rutgers University
2 Bowdoin College 
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     title = {Modular statistics for subgraph counts in sparse random graphs},
     journal = {The electronic journal of combinatorics},
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Bobby DeMarco; Jeff Kahn; Amanda Redlich. Modular statistics for subgraph counts in sparse random graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4094

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