# 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}. - published version (9p)

Bib entry

@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}, doi = {10.1007/BF02188208}, mrclass = {05C15 (03E05 03E35)}, mrnumber = {1374388}, mrreviewer = {E. C. Milner}, doi = {10.1007/BF02188208}, note = {\href{https://arxiv.org/abs/math/9402213}{arXiv: math/9402213}}, arxiv_number = {math/9402213} }