{"paper":{"title":"On universal graphs without cliques or withour large bipartite graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Menachem Kojman","submitted_at":"1995-07-18T00:00:00Z","abstract_excerpt":"For every uncountable cardinal $\\lambda$, suitable negations of the Generalized Continuum Hypothesis imply:\n - For all infinite $\\alpha$ and $\\beta$, there is no universal $K_{\\alpha,\\beta}$-free graphs in $\\lambda$\n - For all $\\alpha\\ge 3$, there is no universal $K_\\alpha$-free graph in $\\lambda$\n  The instance $K_{\\omega,\\omega_1}$ for $\\lambda=\\aleph_1$ was settled by Komjath and Pach from the principle $\\diamondsuit(\\omega_1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507211","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}