The relative clique-width of a graph

Journal of Combinatorial Theory. Series B

Volumn 97, Issue 5, 2007, Pages 846-858

  Lozin, Vadim ^a   Rautenbach, Dieter ^b  

^a RUTGERS UNIVERSITY   (United States)

^b ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Approximation algorithm; Chromatic number; Clique width; Coloring; Tree decompositions; Tree width

Indexed keywords

EID: 34447297816     PISSN: 00958956     EISSN: 10960902     Source Type: Journal    
DOI: 10.1016/j.jctb.2007.04.001     Document Type: Article

References (20)

1. Bodlaender H.L. A partial k-arboretum of graphs with bounded treewidth. Theoret. Comput. Sci. 209 (1998) 1-45
2. Bodlaender H.L. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25 (1996) 1305-1317
3. Bodlaender H.L. Treewidth: Algorithmic techniques and results. Lecture Notes in Comput. Sci. vol. 1295 (1997), Springer, Berlin 19-36
4. Corneil D.G., and Rotics U. On the relationship between clique-width and treewidth (extended abstract). Lecture Notes in Comput. Sci. 2204 (2001) 78-90
5. Courcelle B. The monadic second-order logic of graphs. III. Tree-decompositions, minors and complexity issues. RAIRO Inform. Théor. Appl. 26 (1992) 257-286
6. Courcelle B. Clique-width of countable graphs: a compactness property. Discrete Math. 276 (2004) 127-148
7. Courcelle B., and Olariu S. Upper bounds to the clique-width of a graph. Discrete Appl. Math. 101 (2000) 77-114
8. Courcelle B., Makowsky J.A., and Rotics U. Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst. 33 (2000) 125-150
9. Courcelle B., Makowsky J.A., and Rotics U. On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Discrete Appl. Math. 108 (2001) 23-52
10. Downey R.G., and Fellows M.R. Parameterized Complexity. Monogr. Comput. Sci. (1999), Springer-Verlag, New York xvi+533 pp
11. M.R. Fellows, F.A. Rosamond, U. Rotics, S. Szeider, Clique-width minimization is NP-hard, in: Proceedings of STOC 2006, 38th ACM Symposium on Theory of Computing, 2006, pp. 354-362
12. Flum J., and Grohe M. Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series (2006), Springer-Verlag, Berlin xiv+493 pp
13. Gurski F., and Wanke E. On the relationship between NLC-width and linear NLC-width. Theoret. Comput. Sci. 347 (2005) 76-89
14. V. Lozin, D. Rautenbach, The relative clique-width of a graph, RUTCOR Research Reports 16-2004, May 2004, available under: http://rutcor.rutgers.edu/pub/rrr/reports2004/16_2004.ps
15. Oum S.-I. Rank-width and vertex-minors. J. Combin. Theory Ser. B 95 (2005) 79-100
16. Oum S.-I., and Seymour P. Approximating clique-width and branch-width. J. Combin. Theory Ser. B 96 (2006) 514-528
17. Perković L., and Reed B. An improved algorithm for finding tree decompositions of small width. Internat. J. Found. Comput. Sci. 11 (2000) 365-371
18. Reed B. Tree width and tangles: a new connectivity measure and some applications. London Math. Soc. Lecture Note Ser. vol. 241 (1997), Cambridge Univ. Press, Cambridge 87-162
19. Robertson N., and Seymour P.D. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms 7 (1986) 309-322
20. Robertson N., and Seymour P.D. Graph minors. X. Obstructions to tree-decomposition. J. Combin. Theory Ser. B 52 (1991) 153-190