{"paper":{"title":"Improved approximation algorithms for path vertex covers in regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"An Zhang, Guohui Lin, Yong Chen, Zhi-Zhong Chen","submitted_at":"2018-11-03T05:05:51Z","abstract_excerpt":"Given a simple graph $G = (V, E)$ and a constant integer $k \\ge 2$, the $k$-path vertex cover problem ({\\sc P$k$VC}) asks for a minimum subset $F \\subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path of order $k$. When $k = 2$, this turns out to be the classic vertex cover ({\\sc VC}) problem, which admits a $\\left(2 - {\\rm \\Theta}\\left(\\frac 1{\\log|V|}\\right)\\right)$-approximation. The general {\\sc P$k$VC} admits a trivial $k$-approximation; when $k = 3$ and $k = 4$, the best known approximation results for {\\sc P$3$VC} and {\\sc P$4$VC} are a $2$-approxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01162","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"}