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- W4287025765 abstract "Estimating the probability that the ErdH{o}s-R'enyi random graph $G(n,m)$ is $H$-free, for a fixed graph $H$, is one of the fundamental problems in random graph theory. If $m$ is such that each edge of $G(n,m)$ belongs to a copy of $H'$ for every $H' subseteq H$, in expectation, then it is known that $G(n,m)$ is $H$-free with probability $exp(- Theta(m))$. The KLR conjecture, slightly rephrased, states that if we further condition on uniform edge distribution, the archetypal property of random graphs, the probability of being $H$-free becomes superexponentially small in the number of edges. While being interesting on its own, the conjecture has received significant attention due to its connection with the sparse regularity lemma, and the many results in random graphs that follow. It was proven by Balogh, Morris, and Samotij and, independently, by Saxton and Thomason, as one of the first applications of the hypergraph containers method. We give a new direct proof using induction." @default.
- W4287025765 created "2022-07-25" @default.
- W4287025765 creator A5074609284 @default.
- W4287025765 date "2021-08-12" @default.
- W4287025765 modified "2023-10-14" @default.
- W4287025765 title "A new proof of the KL R conjecture" @default.
- W4287025765 doi "https://doi.org/10.48550/arxiv.2108.05687" @default.
- W4287025765 hasPublicationYear "2021" @default.
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