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arXiv · 1305.2516

On the K{\L}R conjecture in random graphs

D. Conlon·W. T. Gowers·W. Samotij·M. Schacht
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Abstract

The K{\L}R conjecture of Kohayakawa, {\L}uczak, and R\"odl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G_{n,p}, for sufficiently large p : = p(n), satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and R\"odl. We prove a variant of this conjecture which is sufficient for most known applications to random graphs. In particular, our result implies a number of recent probabilistic versions, due to Conlon, Gowers, and Schacht, of classical extremal combinatorial theorems. We also discuss several further applications.

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BibTeXRIS

D. Conlon, W. T. Gowers, W. Samotij, M. Schacht. 2013-05-11. On the K{\L}R conjecture in random graphs. https://doi.org/10.1007/s11856-014-1120-1

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