On Taylor's problem
Logic
2016-09-06 v1
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} .
Cite
@article{arxiv.math/9402213,
title = {On Taylor's problem},
author = {Peter Komjath and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9402213},
year = {2016}
}