Feedback Set Problems on Bounded-Degree (Planar) Graphs
摘要
The 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 -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 -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.
引用
@article{arxiv.2605.11407,
title = {Feedback Set Problems on Bounded-Degree (Planar) Graphs},
author = {Tian Bai and Yixin Cao and Mingyu Xiao},
journal= {arXiv preprint arXiv:2605.11407},
year = {2026}
}