{"paper":{"title":"Ramsey goodness of complete multipartite graphs with one large part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shaonan Mi, Ye Wang","submitted_at":"2026-05-26T10:44:17Z","abstract_excerpt":"For graph $G$, a connected graph $H$ of order $n$ is said to be $G$-good if $r(G,H)=(\\chi(G)-1)(n-1)+s(G)$, where $\\chi(G)$ is the chromatic number of $G$ and $s(G)$ is the minimum size of a color class in a $\\chi(G)$-coloring of $G$. Let $K_{p+1}(\\alpha;n)$ denote the complete $(p+1)$-partite graph with $p$ partite sets of size $\\alpha$ and one partite set of size $n$. We determine all graphs $G$ for which $K_{p+1}(\\alpha;n)$ is $G$-good for large $n$. The characterization depends on the parameter $\\mathrm{snd}(\\alpha)$, the smallest non-divisor of $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26826","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26826/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}