{"paper":{"title":"Phylogenetic flexibility via Hall-type inequalities and submodularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katharina T. Huber, Mike Steel, Vincent Moulton","submitted_at":"2017-10-24T18:51:17Z","abstract_excerpt":"Given a collection $\\tau$ of subsets of a finite set $X$, we say that $\\tau$ is {\\em phylogenetically flexible} if, for any collection $R$ of rooted phylogenetic trees whose leaf sets comprise the collection $\\tau$, $R$ is compatible (i.e. there is a rooted phylogenetic $X$--tree that displays each tree in $R$). We show that $\\tau$ is phylogenetically flexible if and only if it satisfies a Hall-type inequality condition of being `slim'. Using submodularity arguments, we show that there is a polynomial-time algorithm for determining whether or not $\\tau$ is slim. This `slim' condition reduces t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08946","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"}