TY - JOUR
T1 - On the KŁR conjecture in random graphs
AU - Conlon, D.
AU - Gowers, W. T.
AU - Samotij, W.
AU - Schacht, M.
N1 - Publisher Copyright: © 2014, Hebrew University of Jerusalem.
PY - 2014/10
Y1 - 2014/10
N2 - The KŁR conjecture of Kohayakawa, Łuczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph Gn,p, for sufficiently large p:= p(n), satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. 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.
AB - The KŁR conjecture of Kohayakawa, Łuczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph Gn,p, for sufficiently large p:= p(n), satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. 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.
UR - http://www.scopus.com/inward/record.url?scp=84933678917&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/s11856-014-1120-1
DO - https://doi.org/10.1007/s11856-014-1120-1
M3 - مقالة
SN - 0021-2172
VL - 203
SP - 535
EP - 580
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -