{"paper":{"title":"On the tractability of some natural packing, covering and partitioning problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Attila Bern\\'ath, Zolt\\'an Kir\\'aly","submitted_at":"2014-07-18T13:47:45Z","abstract_excerpt":"In this paper we fix 7 types of undirected graphs: paths, paths with prescribed endvertices, circuits, forests, spanning trees, (not necessarily spanning) trees and cuts. Given an undirected graph $G=(V,E)$ and two \"object types\" $\\mathrm{A}$ and $\\mathrm{B}$ chosen from the alternatives above, we consider the following questions. \\textbf{Packing problem:} can we find an object of type $\\mathrm{A}$ and one of type $\\mathrm{B}$ in the edge set $E$ of $G$, so that they are edge-disjoint? \\textbf{Partitioning problem:} can we partition $E$ into an object of type $\\mathrm{A}$ and one of type $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4999","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"}