{"paper":{"title":"Ramsey-nice families of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Naor, Dan Hefetz, Gal Kronenberg, Michal Amir, Noga Alon, Penny Haxell, Ron Aharoni, Zilin Jiang","submitted_at":"2017-08-24T12:14:51Z","abstract_excerpt":"For a finite family $\\mathcal{F}$ of fixed graphs let $R_k(\\mathcal{F})$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\\in\\mathcal{F}$. We say that $\\mathcal{F}$ is $k$-nice if for every graph $G$ with $\\chi(G)=R_k(\\mathcal{F})$ and for every $k$-coloring of $E(G)$ there exists a monochromatic copy of some $F\\in\\mathcal{F}$. It is easy to see that if $\\mathcal{F}$ contains no forest, then it is not $k$-nice for any $k$. It seems plausible to conjecture that a (weak) converse holds, namely, for any finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07369","kind":"arxiv","version":2},"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"}