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  "path": "/abs/2605.11407v1",
  "publishedAt": "2026-05-13T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Tian Bai",
    "Yixin Cao",
    "Mingyu Xiao"
  ],
  "textContent": "**Authors:** Tian Bai, Yixin Cao, Mingyu Xiao\n\nThe feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We obtain a complete complexity classification for these problems on bounded-degree digraphs, including the planar case. In particular, we show that both problems are $\\NP$-complete on digraphs of maximum degree three, while on planar digraphs the feedback vertex set problem is polynomial-time solvable when each vertex has either indegree at most one or outdegree at most one, and $\\NP$-complete otherwise. We also give tight degree bounds for the connected feedback vertex set problem on undirected graphs, both planar and non-planar. We close the paper with a historical account of results for feedback vertex set on undirected graphs of bounded degree.",
  "title": "Feedback Set Problems on Bounded-Degree (Planar) Graphs"
}