{"paper":{"title":"Simultaneous Feedback Edge Set: A Parameterized Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akanksha Agrawal, Fahad Panolan, Meirav Zehavi, Saket Saurabh","submitted_at":"2016-11-23T09:32:46Z","abstract_excerpt":"In this paper we consider Simultaneous Feedback Edge Set (Sim-FES) problem. In this problem, the input is an $n$-vertex graph $G$, an integer $k$ and a coloring function ${\\sf col}: E(G) \\rightarrow 2^{[\\alpha]}$ and the objective is to check whether there is an edge subset $S$ of cardinality at most $k$ in $G$ such that for all $i \\in [\\alpha]$, $G_i - S$ is acyclic. Here, $G_i=(V(G), \\{e\\in E(G) \\mid i \\in {\\sf col}(e)\\})$ and $[\\alpha]=\\{1,\\ldots,\\alpha\\}$. When $\\alpha =1$, the problem is polynomial time solvable. We show that for $\\alpha =3$ Sim-FES is NP-hard by giving a reduction from V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07701","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"}