{"paper":{"title":"On edges not in monochromatic copies of a fixed bipartite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma","submitted_at":"2016-05-30T08:57:10Z","abstract_excerpt":"Let $H$ be a fixed graph. Denote $f(n,H)$ to be the maximum number of edges not contained in any monochromatic copy of $H$ in a 2-edge-coloring of the complete graph $K_n$, and $ex(n,H)$ to be the {\\it Tur\\'an number} of $H$. An easy lower bound shows $f(n,H)\\ge ex(n,H)$ for any $H$ and $n$. In \\cite{KS2}, Keevash and Sudakov proved that if $H$ is an edge-color-critical graph or $C_4$, then $f(n,H)= ex(n,H)$ holds for large $n$, and they asked if this equality holds for any graph $H$ when $n$ is sufficiently large. In this paper, we provide an affirmative answer to this problem for an abundant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09141","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"}