On Minimum Feedback Vertex Sets in Bipartite Graphs and Degree-Constraint Graphs

Asahi TAKAOKA  Satoshi TAYU  Shuichi UENO  

IEICE TRANSACTIONS on Information and Systems   Vol.E96-D   No.11   pp.2327-2332
Publication Date: 2013/11/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E96.D.2327
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
3-regular graph,  bipartite permutation graph,  feedback vertex set,  grid intersection graph,  nonseparating independent set,  

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We consider the minimum feedback vertex set problem for some bipartite graphs and degree-constrained graphs. We show that the problem is linear time solvable for bipartite permutation graphs and NP-hard for grid intersection graphs. We also show that the problem is solvable in O(n2log 6n) time for n-vertex graphs with maximum degree at most three.