{"paper":{"title":"Minimum k-path vertex cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Bo\\v{s}tjan Bre\\v{s}ar, Franti\\v{s}ek Kardo\\v{s}, Gabriel Semani\\v{s}in, J\\'an Katreni\\v{c}","submitted_at":"2010-12-09T19:25:09Z","abstract_excerpt":"A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by \\psi_k(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining \\psi_k(G) is NP-hard for each k \\geq 2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of \\psi_k(G) and provide several estimations and exact values of \\psi_k(G). We also prove that \\psi_3(G) \\leq (2n + m)/6, for every graph G with n vertices and m edges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2088","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"}