{"paper":{"title":"On a conjecture of compatibility of multi-states characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"cs.DS","authors_text":"Michel Habib, Thu-Hien To","submitted_at":"2011-05-05T15:58:02Z","abstract_excerpt":"Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete. We propose in this article a conjecture on the necessary and sufficient conditions of compatibility: Given a set $\\mathcal{C}$ of $r$-states full characters, there exists a function $f(r)$ such that $\\mathcal{C}$ is compatible iff every set of $f(r)$ characters of $\\mathcal{C}$ is compatible. Some previous work showed that $f(2)=2$, $f(3)=3$ and $f(r) \\ge r-1$. Gusfield et al. 09 conjectured that $f(r) = r$ for any $r \\ge 2$. In this paper, we present an example showing that $f(4) \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1109","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"}