Sh:346

• Komjáth, P., & Shelah, S. (1996). On Taylor’s problem. Acta Math. Hungar., 70(3), 217–225. arXiv: math/9402213 DOI: 10.1007/BF02188208 MR: 1374388
• Abstract:
  We describe some (countably many) classes K^{n,e} of finite graphs and prove that if \lambda^{\aleph_0}=\lambda then every \lambda^+-chromatic graph of cardinal \lambda^+ contains, for some n, e, all members of K^{n,e} as subgraphs. On the other hand, it is consistent for every regular infinite cardinal \kappa that there is a \kappa^+-chromatic graph on \kappa^+ that contains finite subgraphs only from K^{n,e}.
• Version 1994-01-31_10 (7p) published version (9p)

@article{Sh:346,
 author = {Komj{\'a}th, P{\'e}ter and Shelah, Saharon},
 title = {{On Taylor's problem}},
 journal = {Acta Math. Hungar.},
 fjournal = {Acta Mathematica Hungarica},
 volume = {70},
 number = {3},
 year = {1996},
 pages = {217--225},
 issn = {0236-5294},
 mrnumber = {1374388},
 mrclass = {05C15 (03E05 03E35)},
 doi = {10.1007/BF02188208},
 note = {\href{https://arxiv.org/abs/math/9402213}{arXiv: math/9402213}},
 arxiv_number = {math/9402213}
}