{"paper":{"title":"Size Ramsey number for star forests","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pingting Fu, Zhenyu Ni, Zhidan Luo","submitted_at":"2026-06-03T04:39:24Z","abstract_excerpt":"For given graphs $G_{1}, G_{2}, \\dots, G_{t}$ and $G$, let $G\\rightarrow (G_{1}, G_{2}, \\dots, G_{t})$ denote that each $t$-coloring of $E(G)$ yields a monochromatic copy of $G_{i}$ in color $i$ for some $i\\in [t]$. The {\\it size Ramsey number} $\\hat{r}(G_{1}, G_{2}, \\dots, G_{t})$ is the minimum size of $G$ such that $G\\rightarrow (G_{1}, G_{2}, \\dots, G_{t})$. A graph $G$ is a {\\it size Ramsey minimal graph} for $(G_{1}, G_{2}, \\dots, G_{t})$ if $G\\rightarrow (G_{1}, G_{2}, \\dots, G_{t})$ and $e(G)= \\hat{r}(G_{1}, G_{2}, \\dots, G_{t})$. A {\\it star forest} is a vertex-disjoint union of stars"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04439","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/2606.04439/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"}