### On incompactness for chromatic number of graphs

by Shelah. [Sh:1006]

Acta Math Hungarica, 2013

We deal with incompactness. Assume the existence of
non-reflecting stationary set of cofinality kappa . We prove
that one can define a graph G whose chromatic number is
> kappa, while the chromatic number of every subgraph G'
subseteq G,|G'| < |G| is <= kappa . The main case is kappa
= aleph_0 .

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