{"paper":{"title":"Towards the fixed parameter tractability of constructing minimal phylogenetic networks from arbitrary sets of nonbinary trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"q-bio.PE","authors_text":"Celine Scornavacca, Steven Kelk","submitted_at":"2012-07-30T18:41:21Z","abstract_excerpt":"It has remained an open question for some time whether, given a set of not necessarily binary (i.e. \"nonbinary\") trees T on a set of taxa X, it is possible to determine in time f(r).poly(m) whether there exists a phylogenetic network that displays all the trees in T, where r refers to the reticulation number of the network and m=|X|+|T|. Here we show that this holds if one or both of the following conditions holds: (1) |T| is bounded by a function of r; (2) the maximum degree of the nodes in T is bounded by a function of r. These sufficient conditions absorb and significantly extend known spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7034","kind":"arxiv","version":2},"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"}