On universal graphs without cliques or withour large bipartite graphs

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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 Kω,ω1 for λ = ℵ1 was settled by Komjath and Pach from the principle ♦(ω1).
Original languageEnglish
PublisherarXiv math/9507211
StatePublished - 1995

Keywords

  • Mathematics - Logic

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