{"paper":{"title":"Improved Kernels and Algorithms for Claw and Diamond Free Edge Deletion Based on Refined Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Huan Peng, Wenjun Li, Yongjie Yang","submitted_at":"2017-07-21T07:19:03Z","abstract_excerpt":"In the {claw, diamond}-free edge deletion problem, we are given a graph $G$ and an integer $k>0$, the question is whether there are at most $k$ edges whose deletion results in a graph without claws and diamonds as induced graphs. Based on some refined observations, we propose a kernel of $O(k^3)$ vertices and $O(k^4)$ edges, significantly improving the previous kernel of $O(k^{12})$ vertices and $O(k^{24})$ edges. In addition, we derive an $O^*(3.792^k)$-time algorithm for the {claw, diamond}-free edge deletion problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06779","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1707.06779/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}