{"paper":{"title":"Finding k partially disjoint paths in a directed planar graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver","submitted_at":"2015-04-01T11:36:09Z","abstract_excerpt":"The {\\it partially disjoint paths problem} is: {\\it given:} a directed graph, vertices $r_1,s_1,\\ldots,r_k,s_k$, and a set $F$ of pairs $\\{i,j\\}$ from $\\{1,\\ldots,k\\}$, {\\it find:} for each $i=1,\\ldots,k$ a directed $r_i-s_i$ path $P_i$ such that if $\\{i,j\\}\\in F$ then $P_i$ and $P_j$ are disjoint.\n  We show that for fixed $k$, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is solvable in polynomial time for directed graphs embedded on a fixed compact surface. Moreover, one may specify for each edge a subset of $\\{1,\\ldots,k\\}$ prescrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00185","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"}