On Taylor's problem
Peter Komjath, Saharon Shelah
Abstract
We describe some (countably many) classes Kn,e of finite graphs and prove that if lambdaaleph0= lambda then every lambda+-chromatic graph of cardinal lambda+ contains, for some n, e, all members of Kn,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 Kn,e .
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