{"paper":{"title":"On the Erd\\\"os-Lov\\'asz Tihany Conjecture for Claw-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandra Fradkin, Maria Chudnovsky, Matthieu Plumettaz","submitted_at":"2013-09-04T13:20:09Z","abstract_excerpt":"In 1968, Erd\\\"os and Lov\\'asz conjectured that for every graph $G$ and all integers $s,t\\geq 2$ such that $s+t-1=\\chi(G) > \\omega(G)$, there exists a partition $(S,T)$ of the vertex set of $G$ such that $\\chi(G|S)\\geq s$ and $\\chi(G|T)\\geq t$. For general graphs, the only settled cases of the conjecture are when $s$ and $t$ are small. Recently, the conjecture was proved for a few special classes of graphs: graphs with stability number 2 \\cite{quasi-line}, line graphs \\cite{line} and quasi-line graphs \\cite{quasi-line}. In this paper, we consider the conjecture for claw-free graphs and present "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1020","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"}