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On universal graphs without cliques or withour large bipartite graphs

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Publication:6503597

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arXivmath/9507211MaRDI QIDQ6503597

Author name not available (Why is that?)

Abstract: For every uncountable cardinal

l a m b d a

, suitable negations of the Generalized Continuum Hypothesis imply: - For all infinite

a l p h a

and

, there is no universal

-free graphs in

l a m b d a

- For all

a l p h a g e 3

, there is no universal

K_{a} l p h a

-free graph in

l a m b d a

The instance

K_{o m e g a, o m e g a_{1}}

for

l a m b d a = a l e p h_{1}

was settled by Komjath and Pach from the principle

d i a m o n d s u i t (o m e g a_{1})

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