Sh:370

• Shelah, S., & Soukup, L. (1994). On the number of nonisomorphic subgraphs. Israel J. Math., 86(1-3), 349–371. arXiv: math/9401210 DOI: 10.1007/BF02773686 MR: 1276143
• Abstract:
  Let \mathcal K be the family of graphs on \omega_1 without cliques or independent subsets of size \omega_1. We prove that:

  1) it is consistent with CH that every G\in{\mathcal K} has 2^{\omega_1} many pairwise non-isomorphic subgraphs,

  2) the following proposition holds in L: (*) there is a G\in{\mathcal K} such that for each partition (A,B) of \omega_1 either G\cong G[A] or G\cong G[B],

  3) the failure of (*) is consistent with ZFC.

• Version 1994-08-30_10 (25p) published version (23p)

@article{Sh:370,
 author = {Shelah, Saharon and Soukup, Lajos},
 title = {{On the number of nonisomorphic subgraphs}},
 journal = {Israel J. Math.},
 fjournal = {Israel Journal of Mathematics},
 volume = {86},
 number = {1-3},
 year = {1994},
 pages = {349--371},
 issn = {0021-2172},
 mrnumber = {1276143},
 mrclass = {03E35 (03E75 05C30)},
 doi = {10.1007/BF02773686},
 note = {\href{https://arxiv.org/abs/math/9401210}{arXiv: math/9401210}},
 arxiv_number = {math/9401210}
}