On universal graphs without cliques or withour large bipartite graphs

Details On universal graphs without cliques or withour large bipartite graphs On universal graphs without cliques or withour large bipartite graphs

1995-07-18

arxiv.org/abs/math/9507211v1

Mathematics

Logic

Scientific paper

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 $\diamondsuit(\omega_1)$.

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