## Abstract

For every uncountable cardinal λ, suitable

negations of the Generalized Continuum Hypothesis imply:

(a) For all infinite α and β, there is no universal Kα,β-free

graphs in λ

(b) For all α ≥ 3, there is no universal Kα-free graph in λ

The instance K

negations of the Generalized Continuum Hypothesis imply:

(a) For all infinite α and β, there is no universal Kα,β-free

graphs in λ

(b) For all α ≥ 3, there is no universal Kα-free graph in λ

The instance K

_{ω,ω1 }for λ = ℵ1 was settled by Komjath and Pach from the principle ♦(ω1).Original language | English |
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Publisher | arXiv math/9507211 |

State | Published - 1995 |

## Keywords

- Mathematics - Logic