On Minimum Feedback Vertex Sets in Graphs

For the minimum feedback vertex set problem, we show a linear time algorithm for bipartite permutation graphs, the NP-hardness for grid intersection graphs, and a polynomial time algorithm for graphs with maximum degree at most three.

[1]  John M. Lewis,et al.  The Node-Deletion Problem for Hereditary Properties is NP-Complete , 1980, J. Comput. Syst. Sci..

[2]  Harold N. Gabow,et al.  An augmenting path algorithm for linear matroid parity , 1986, Comb..

[3]  Yoji Kajitani,et al.  On the nonseparating independent set problem and feedback set problem for graphs with no vertex degree exceeding three , 1988, Discret. Math..

[4]  Harold N. Gabow,et al.  Efficient Algorithms for Graphic Intersection and Parity (Extended Abstract) , 1985 .

[5]  Toshinori Yamada,et al.  The undirected feedback vertex set problem with application to wavelength converter placement on WDM networks , 2010, 2010 XIth International Workshop on Symbolic and Numerical Methods, Modeling and Applications to Circuit Design (SM2ACD).

[6]  Matthias F. Stallmann,et al.  Efficient Algorithms for Graphic Matroid Intersection and Parity (Extended Abstract) , 1985, ICALP.

[7]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[8]  Jonathan L. Gross,et al.  Finding a maximum-genus graph imbedding , 1988, JACM.

[9]  Ilan Newman,et al.  On grid intersection graphs , 1991, Discret. Math..

[10]  Maw-Shang Chang,et al.  Minimum feedback vertex sets in cocomparability graphs and convex bipartite graphs , 1997, Acta Informatica.

[11]  Y. Daniel Liang On the Feedback Vertex Set Problem in Permutation Graphs , 1994, Inf. Process. Lett..

[12]  David S. Johnson,et al.  The Rectilinear Steiner Tree Problem is NP Complete , 1977, SIAM Journal of Applied Mathematics.

[13]  Mihalis Yannakakis,et al.  Node-Deletion Problems on Bipartite Graphs , 1981, SIAM J. Comput..

[14]  Yanpei Liu,et al.  Maximum genus and maximum nonseparating independent set of a 3-regular graph , 1997, Discret. Math..

[15]  K. Onaga,et al.  Vertex covers and connected vertex covers in 3-connected graphs , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[16]  Jeremy P. Spinrad,et al.  Bipartite permutation graphs , 1987, Discret. Appl. Math..

[17]  Sue Whitesides,et al.  Grid intersection graphs and boxicity , 1993, Discret. Math..

[18]  Ewald Speckenmeyer,et al.  Untersuchungen zum Feedback-vertex-set-Problem in ungerichteten Graphen , 1983 .

[19]  T. Kloks,et al.  Feedback vertex set on chordal bipartite graphs , 2011, 1104.3915.

[20]  Satoshi Tayu,et al.  On orthogonal ray graphs , 2010, Discret. Appl. Math..

[21]  Panos M. Pardalos,et al.  Feedback Set Problems , 2009, Encyclopedia of Optimization.