{"paper":{"title":"Exact Algorithms for Edge Deletion to Cactus Graphs and Weighted Variants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Wenhao Song","submitted_at":"2026-06-16T06:27:51Z","abstract_excerpt":"We study exact exponential-time algorithms for Edge Deletion to Cactus. Given a connected graph $G$, the task is to delete a minimum number of edges so that the remaining spanning graph is a connected cactus. Akhtar and Philip (IWOCA 2026) gave an $O^*(3^n)$-time algorithm for the unweighted problem, where $n$ is the number of vertices in the input graph and the $O^*(\\cdot)$ notation hides polynomial factors.\n  We improve this bound to $O^*(2^n)$ time and space. More generally, if the deletion costs take at most $q$ distinct nonnegative real values, then the weighted problem can be solved in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17578","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17578/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"}