{"paper":{"title":"Anti-Ramsey Numbers for Spanning Linear Forests of 3-Vertex Paths and Matchings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Ghalavand, Xueliang Li","submitted_at":"2025-09-30T08:44:23Z","abstract_excerpt":"A subgraph in an edge-colored graph is called rainbow if all its edges have distinct colors. For a graph $G$ and an integer $n$, the anti-Ramsey number $AR(n,G)$ is the maximum number of colors in an edge-coloring of $K_n$ that contains no rainbow copy of $G$. We study $AR(n, kP_3 \\cup tP_2)$, where $kP_3 \\cup tP_2$ is the linear forest of $k$ disjoint paths on three vertices and a matching of size $t$. Recently, Jie and Jin [Discrete Appl. Math. 386 (2026) 30-57] determined this number for $k\\geq 2$, $t\\geq\\frac{k^2-3k+4}{2}$ and $n=2t+3k$. Here we solve the spanning case $n=3k+2t$ for all $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.25949","kind":"arxiv","version":3},"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"}