From a Circular-Arc Model to a Proper Circular-Arc Model

We are given a circular-arc graph, represented by a circular-arc model; our goal is to decide whether the graph is a proper circular-arc graph. We do so in time linear in the number of vertices of the graph, regardless of the number of edges which may be quadratic in the number of vertices. For every input graph, we either provide a proper circular-arc model for the graph, or a forbidden subgraph induced in the graph.

[1]  Jayme Luiz Szwarcfiter,et al.  Linear-Time Recognition of Helly Circular-Arc Models and Graphs , 2011, Algorithmica.

[2]  Peter L. Hammer,et al.  Difference graphs , 1990, Discret. Appl. Math..

[3]  Jeremy P. Spinrad,et al.  Efficient graph representations , 2003, Fields Institute monographs.

[4]  Ross M. McConnell.  Linear-Time Recognition of Circular-Arc Graphs , 2003, Algorithmica.

[5]  Lars Arge,et al.  Algorithm Theory - SWAT 2006, 10th ScandinavianWorkshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006, Proceedings , 2006, SWAT.

[6]  M. Golumbic.  Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57) , 2004 .

[7]  Glenn K. Manacher,et al.  A simple linear time algorithm for finding a maximum independent set of circular arcs using intervals alone , 2002, Networks.

[8]  Alan Tucker,et al.  Structure theorems for some circular-arc graphs , 1974, Discret. Math..

[9]  Haim Kaplan,et al.  A Simpler Linear-Time Recognition of Circular-Arc Graphs , 2006, SWAT.

[10]  Wen-Lian Hsu,et al.  An O(n1.5) algorithm to color proper circular arcs , 1989, Discret. Appl. Math..

[11]  Jayme Luiz Szwarcfiter,et al.  Proper Helly Circular-Arc Graphs , 2007, WG.

[12]  Xiaotie Deng,et al.  Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs , 1996, SIAM J. Comput..

[13]  Peter L. Hammer,et al.  Stability in Circular Arc Graphs , 1988, J. Algorithms.

[14]  Wen-Lian Hsu,et al.  Linear Time Algorithms on Circular-Arc Graphs , 1991, Inf. Process. Lett..

[15]  Haim Kaplan,et al.  Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs , 2009, Discret. Appl. Math..

[16]  Wen-Lian Hsu.  O(M*N) Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs , 1995, SIAM J. Comput..

[17]  Jayme Luiz Szwarcfiter,et al.  Efficient construction of unit circular-arc models , 2006, SODA '06.

[18]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[19]  Alan C. Tucker,et al.  An Efficient Test for Circular-Arc Graphs , 1980, SIAM J. Comput..

[20]  Kazuo Nakajima,et al.  An Optimal Algorithm for Finding a Maximum Independent Set of a Circular-Arc Graph , 1988, SIAM J. Comput..