{"paper":{"title":"Disjoint paths in unions of tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Maria Chudnovsky, Paul Seymour","submitted_at":"2016-04-08T11:55:23Z","abstract_excerpt":"Given $k$ pairs of vertices $(s_i,t_i)\\;(1\\le i\\le k)$ of a digraph $G$, how can we test whether there exist vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\\le i\\le k$? This is NP-complete in general digraphs, even for $k = 2$, but in an earlier paper we proved that for all fixed $k$, there is a polynomial-time algorithm to solve the problem if $G$ is a tournament (or more generally, a semicomplete digraph). Here we prove that for all fixed $k$ there is a polynomial-time algorithm to solve the problem when $V(G)$ is partitioned into a bounded number of sets each inducing a semicomple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02317","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"}