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- W2890424150 abstract "For given integers $k$ and $ell$ with $0<ell< {k choose 2}$, Alon, Hefetz, Krivelevich and Tyomkyn formulated the following conjecture: When sampling a $k$-vertex subset uniformly at random from a very large graph $G$, then the probability to have exactly $ell$ edges within the sampled $k$-vertex subset is at most $e^{-1}+o_k(1)$. This conjecture was proved in the case $Omega(k)leq ellleq {k choose 2}-Omega(k)$ by Kwan, Sudakov and Tran. In this paper, we complete the proof of the conjecture by resolving the remaining cases. We furthermore give nearly tight upper bounds for the probability described above in the case $omega(1)leq ellleq o(k)$. We also extend some of our results to hypergraphs with bounded edge size." @default.
- W2890424150 created "2018-09-27" @default.
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- W2890424150 date "2018-09-05" @default.
- W2890424150 modified "2023-09-27" @default.
- W2890424150 title "A Completion of the Proof of the Edge-statistics Conjecture" @default.
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