# Sh:627

- Shelah, S. (1998).
*Erdős and Rényi conjecture*. J. Combin. Theory Ser. A,**82**(2), 179–185. arXiv: math/9707226 DOI: 10.1006/jcta.1997.2845 MR: 1620869 -
Abstract:

Affirming a conjecture of Erdös and Rényi we prove that for any (real number) c_1>0 for some c_2>0, if a graph G has no c_1(\log n) nodes on which the graph is complete or edgeless (i.e. G exemplifies |G|\not\rightarrow (c_1\log n)^2_2) then G has at least 2^{c_2n} non-isomorphic (induced) subgraphs. - published version (7p)

Bib entry

@article{Sh:627, author = {Shelah, Saharon}, title = {{Erd{\H{o}}s and R{\'e}nyi conjecture}}, journal = {J. Combin. Theory Ser. A}, fjournal = {Journal of Combinatorial Theory. Series A}, volume = {82}, number = {2}, year = {1998}, pages = {179--185}, issn = {0097-3165}, doi = {10.1006/jcta.1997.2845}, mrclass = {05C99}, mrnumber = {1620869}, mrreviewer = {Zbigniew Palka}, doi = {10.1006/jcta.1997.2845}, note = {\href{https://arxiv.org/abs/math/9707226}{arXiv: math/9707226}}, arxiv_number = {math/9707226} }