Author(s)

Hirotoshi Honma, Yoko Nakajima, Atsushi Sasaki

Department of Creative Engineering, National Institute of Technology, Kushiro College, Kushiro, Japan.

The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes  time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.

Design and Analysis of Algorithms, Feedback Vertex Set, Normal Helly Circular-Arc Graphs, Intersection Graphs

Honma, H. , Nakajima, Y. and Sasaki, A. (2016) An Algorithm for the Feedback Vertex Set Problem on a Normal Helly Circular-Arc Graph. Journal of Computer and Communications, 4, 23-31. doi: 10.4236/jcc.2016.48003.