{"paper":{"title":"Linear Kernels for Separating a Graph into Components of Bounded Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mingyu Xiao","submitted_at":"2016-08-20T13:02:58Z","abstract_excerpt":"Graph separation and partitioning are fundamental problems that have been extensively studied both in theory and practice. The \\textsc{$p$-Size Separator} problem, closely related to the \\textsc{Balanced Separator} problem, is to check whether we can delete at most $k$ vertices in a given graph $G$ such that each connected component of the remaining graph has at most $p$ vertices. This problem is NP-hard for each fixed integer $p\\geq 1$ and it becomes the famous \\textsc{Vertex Cover} problem when $p=1$. It is known that the problem with parameter $k$ is W[1]-hard for unfixed $p$. In this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05816","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"}