Feedback vertex sets in star graphs

In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for star graphs. Also by applying the properties of regular graphs, a lower bound can easily be achieved for star graphs.

[1]  David Peleg,et al.  Feedback vertex set in hypercubes , 2000, Inf. Process. Lett..

[2]  Chuan Yi Tang,et al.  A Linear-Time Algorithm for the Weighted Feedback Vertex Problem on Interval Graphs , 1997, Inf. Process. Lett..

[3]  S. Arumugam,et al.  Domination parameters of star graph , 1996, Ars Comb..

[4]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[5]  S. Lakshmivarahan,et al.  Embedding of cycles and Grids in Star Graphs , 1991, J. Circuits Syst. Comput..

[6]  Piotr Berman,et al.  A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem , 1999, SIAM J. Discret. Math..

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

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Mary Lou Soffa,et al.  Feedback vertex sets and cyclically reducible graphs , 1985, JACM.

[10]  Ioannis Caragiannis,et al.  New bounds on the size of the minimum feedback vertex set in meshes and butterflies , 2002, Inf. Process. Lett..

[11]  Peter Baer Galvin,et al.  Applied Operating System Concepts , 1999 .

[12]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

[13]  Abraham Silberschatz,et al.  Operating Systems Concepts , 2005 .

[14]  David S. Johnson,et al.  Computers and Inrracrobiliry: A Guide ro the Theory of NP-Completeness , 1979 .

[15]  Flaminia L. Luccio.  Almost Exact Minimum Feedback Vertex Set in Meshes and Butterflies , 1998, Inf. Process. Lett..

[16]  Peter J. Slater,et al.  Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[17]  Adi Shamir,et al.  A Linear Time Algorithm for Finding Minimum Cutsets in Reducible Graphs , 1979, SIAM J. Comput..