NP-completeness results for edge modification problems

The aim of edge modification problems is to change the edge set of a given graph as little as possible in order to satisfy a certain property. Edge modification problems in graphs have a lot of applications in different areas, and many polynomial-time algorithms and NP-completeness proofs for this kind of problems are known. In this work we prove new NP-completeness results for these problems in some graph classes, such as interval, circular-arc, permutation, circle, bridged, weakly chordal and clique-Helly graphs.

[1]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[2]  Jayme Luiz Szwarcfiter,et al.  Recognizing Clique-Helly Graphs , 1997, Ars Comb..

[3]  Hans L. Bodlaender,et al.  On Intervalizing K-colored Graphs for DNA Physical Mapping , 1996, Discret. Appl. Math..

[4]  Jeremy P. Spinrad,et al.  Polynomial time recognition of unit circular-arc graphs , 2006, J. Algorithms.

[5]  Jeremy P. Spinrad,et al.  Recognition of Circle Graphs , 1994, J. Algorithms.

[6]  Haim Kaplan,et al.  Four Strikes Against Physical Mapping of DNA , 1995, J. Comput. Biol..

[7]  Erich Prisner,et al.  Bicliques in Graphs II: Recognizing k-Path Graphs and Underlying Graphs of Line Digraphs , 1997, WG.

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

[9]  Peter L. Hammer,et al.  The splittance of a graph , 1981, Comb..

[10]  Paul D. Seymour,et al.  Recognizing Berge Graphs , 2005, Comb..

[11]  Ronald C. Read,et al.  Graph theory and computing , 1972 .

[12]  M. Yannakakis.  Computing the Minimum Fill-in is NP^Complete , 1981 .

[13]  François Margot,et al.  Some Complexity Results about Threshold Graphs , 1994, Discret. Appl. Math..

[14]  Jeremy P. Spinrad,et al.  Algorithms for Weakly Triangulated Graphs , 1995, Discret. Appl. Math..

[15]  Mihalis Yannakakis,et al.  Edge-Deletion Problems , 1981, SIAM J. Comput..

[16]  Roded Sharan,et al.  Complexity classification of some edge modification problems , 1999, Discret. Appl. Math..

[17]  D. Rose.  A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS , 1972 .

[18]  Jayme Luiz Szwarcfiter,et al.  Clique Graphs of Chordal and Path Graphs , 1994, SIAM J. Discret. Math..

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

[20]  Flavia Bonomo,et al.  Coordinated graphs and clique graphs of clique-Helly perfect graphs , 2007 .

[21]  Ross M. McConnell,et al.  Linear-Time Recognition of Circular-Arc Graphs , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[22]  Charles J. Colbourn,et al.  The complexity of some edge deletion problems , 1988 .

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

[24]  Guillermo Durán,et al.  Some new results on circle graphs , 2002 .

[25]  M. Golumbic,et al.  On the Complexity of DNA Physical Mapping , 1994 .

[26]  Ben Dushnik,et al.  Partially Ordered Sets , 1941 .

[27]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .

[28]  Jeremy P. Spinrad,et al.  Linear-time transitive orientation , 1997, SODA '97.

[29]  C. Lekkeikerker,et al.  Representation of a finite graph by a set of intervals on the real line , 1962 .

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

[31]  Martin Farber,et al.  On local convexity in graphs , 1987, Discret. Math..

[32]  Min Chih Lin,et al.  Clique graphs of Helly circular arc graphs , 2001, Ars Comb..

[33]  S. Louis Hakimi,et al.  Orienting Graphs to Optimize Reachability , 1997, Inf. Process. Lett..

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

[35]  Erich Prisner,et al.  Bicliques in Graphs I: Bounds on Their Number , 2000, Comb..

[36]  Flavia Bonomo,et al.  Computational complexity of edge modification problems in different classes of graphs , 2004, Electron. Notes Discret. Math..