On universal graphs without cliques or withour large bipartite graphs

Abstract

For every uncountable cardinal $\lambda$, suitable negations of the Generalized Continuum Hypothesis imply: - For all infinite $\alpha$ and $\beta$, there is no universal $K_{\alpha ,\beta }$-free graphs in $\lambda$ - For all $\alpha \ge 3$, there is no universal $K_{\alpha }$-free graph in $\lambda$ The instance $K_{\omega ,{\omega }_1}$ for $\lambda ={\aleph }_1$ was settled by Komjath and Pach from the principle $♢({\omega }_1)$.

References in corpus (1)

• Universal graphs without large cliques

Cited by in corpus (1)

• Representing embeddability as set inclusion