### L. Soukup:

##
Smooth graphs

A graph `G` on `omega_1` is called *<omega-smooth *
if for each uncountable subset `W` of `omega_1`,
`G` is isomorphic to `G[W-W']` for some finite `W'`.
We show that in various models
of ZFC if a graph `G` is `<omega`-smooth then G is
necessarily trivial, i.e, either complete or empty.
On the other hand, we prove that the existence of a non-trivial,
`<omega`-smooth graph is also consistent with ZFC.

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