{"paper":{"title":"On the Computational Complexity of Vertex Integrity and Component Order Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Markus Sortland Dregi, P{\\aa}l Gr{\\o}n{\\aa}s Drange, Pim van 't Hof","submitted_at":"2014-03-25T13:11:09Z","abstract_excerpt":"The Weighted Vertex Integrity (wVI) problem takes as input an $n$-vertex graph $G$, a weight function $w:V(G)\\to\\mathbb{N}$, and an integer $p$. The task is to decide if there exists a set $X\\subseteq V(G)$ such that the weight of $X$ plus the weight of a heaviest component of $G-X$ is at most $p$. Among other results, we prove that:\n  (1) wVI is NP-complete on co-comparability graphs, even if each vertex has weight $1$;\n  (2) wVI can be solved in $O(p^{p+1}n)$ time;\n  (3) wVI admits a kernel with at most $p^3$ vertices.\n  Result (1) refutes a conjecture by Ray and Deogun and answers an open q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6331","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"}