### On Taylor's Problem

by Komjath and Shelah. [KoSh:346]

Acta Math Hungarica, 1996

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} .

Back to the list of publications