Clique-width for 4-vertex forbidden subgraphs

Theory of Computing Systems

Volumn 39, Issue 4, 2006, Pages 561-590

  Brandstadt, Andreas ^a   Engelfriet, Joost ^b   Le, Hoang Oanh ^c   Lozin, Vadim V ^d  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b LEIDEN UNIVERSITY   (Netherlands)

^c BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

^d RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED TREEWIDTH; CLIQUE-WIDTH; COMPLETE CLASSIFICATION; FORBIDDEN INDUCED SUBGRAPHS; FORBIDDEN SUBGRAPHS; GRAPH ALGORITHMS; GRAPH CLASS; TREE-WIDTH;

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

GRAPH THEORY;

EID: 33745046651     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-005-1199-1     Document Type: Article

References (35)

1. R. Boliac and V.V. Lozin, On the clique-width of graphs in hereditary classes, Proceedings of ISAAC 2002, Lecture Notes in Computer Science 2518, Springer-Verlag, Berlin, 2002, pp. 44-54.
2. 5, diamond)-free graphs revisited: structure and linear time optimization, Discrete Appl. Math. 138 (2004), 13-27.
3. A. Brandstädt, F.F. Dragan, H.-O. Le and R. Mosca, New graph classes of bounded clique-width, Theory Comput. Systems 38 (2005), 623-645.
4. A. Brandstädt, C.T. Hoàng and V.B. Le, Stability number of bull- and chair-free graphs revisited, Discrete Appl. Math. 131 (2003), 39-50.
5. 5, gem)-free graphs, Discrete Appl. Math. 145 (2005), 155-166.
6. A. Brandstädt, H.-O. Le and R. Mosca, Gem- and co-gem-free graphs have bounded clique-width, Internat. J. Found. Comput. Sci. 15 (2004), 163-185.
7. 5, gem)-free graphs have bounded clique-width, Discrete Appl. Math. 145 (2005), 232-241.
8. A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, Vol. 3, SIAM, Philadelphia, PA, 1999.
9. A. Brandstädt, H.-O. Le and J.-M. Vanherpe, Structure and stability number of (chair, co-P, gem)-free graphs, Inform. Process. Lett. 86 (2003), 161-167.
10. A. Brandstädt and V.V. Lozin, On the linear structure and clique-width of bipartite permutation graphs, Ars Combin. LXVII (2003), 273-281.
11. A. Brandstädt and S. Mahfud, Maximum weight stable set on graphs without claw and co-claw (and similar graph classes) can be solved in linear time, Inform. Process. Lett. 84 (2002), 251-259.
12. 4-sparse graphs, Discrete Appl. Math. 129 (2003), 521-532.
13. 5- and co-chair-free graphs, Discrete Appl. Math. 132 (2004), 47-65.
14. D.G. Corneil, H. Lerchs and L.K. Stewart-Burlingham, Complement reducible graphs, Discrete Appl. Math. 3 (1981), 163-174.
15. D.G. Corneil, Y. Perl and L.K. Stewart, Cographs: recognition, applications, and algorithms, Congr. Numer. 43 (1984), 249-258.
16. D.G. Corneil, Y. Perl and L.K. Stewart, A linear recognition algorithm for cographs, SIAM J. Comput. 14 (1985), 926-934.
17. B. Courcelle, J. Engelfriet and G. Rozenberg, Handle-rewriting hypergraph grammars, J. Comput. System Sci., 46 (1993), 218-270.
18. B. Courcelle, J.A. Makowsky and U. Rotics, Linear time solvable optimization problems on graphs of bounded clique width, Theory Comput. Systems 33 (2000), 125-150.
19. B. Courcelle and S. Olariu, Upper bounds to the clique-width of graphs, Discrete Appl. Math. 101 (2000), 77-114.
20. M. Farber, Characterizations of strongly chordal graphs, Discrete Math. 43 (1983), 173-189.
21. S. Földes and P.L. Hammer, Split graphs, Congr. Numer. 19 (1977), 311-315.
22. J.-L. Fouquet, V. Giakoumakis and J.-M. Vanherpe, Bipartite graphs totally decomposable by canonical decomposition, Internat. J. Found. Comput. Sci. 10 (1999), 513-533.
23. A.M. Gleason and R.E. Greenwood, Combinatorial relations and chromatic graphs, Canad. J. Math. 7 (1955), 1-7.
24. M.C. Golumbic and U. Rotics, On the clique-width of some perfect graph classes, Internat. J. Found. Comput. Sci. 11 (2000), 423-443.
25. Ö. Johansson, Clique-decomposition, NLC-decomposition, and modular decomposition - relationships and results for random graphs, Congr. Numer. 132 (1998), 39-60; http://www.nada.kth.se/~ojvind/papers/CGTC98.pdf.
26. V.V. Lozin, Bipartite graphs without a skew star, Disante Math. 257 (2002), 83-100.
27. 4's, Internat. J. Found. Comput. Sci. 10 (1999), 329-348.
28. R.M. McConnell and J.P. Spinrad, Modular decomposition and transitive orientation, Discrete Math. 201 (1999), 189-241.
29. G.J. Minty, On maximal independent sets of vertices in claw-free graphs, J. Combin. Theory Ser. B 28 (1980), 284-304.
30. R.H. Möhring and F.J. Radermacher, Substitution decomposition for discrete structures and connections with combinatorial optimization, Ann. Discrete Math. 19 (1984), 257-356.
31. Sang-il Oum, Personal communication, 2004.
32. B. Randerath, The Vizing bound for the chromatic number based on forbidden pairs, Dissertation Thesis, RWTH Aachen, 1998.
33. B. Randerath, I. Schiermeyer and M. Tewes, Three-colourability andforbidden subgraphs, II: polynomial algorithms, Discrete Math. 251 (2002), 137-153.
34. N. Sbihi, Algorithme de recherche d'un stable de cardinalité maximum dans un graphe sans étoile, Discrete Math. 29 (1980), 53-76.
35. M. Yannakakis, The complexity of the partial order dimension problem, SIAM J. Algebraic Discrete Methods 3 (1982), 351-358.