On the band-, tree-, and clique-width of graphs with bounded vertex degree

SIAM Journal on Discrete Mathematics

Volumn 18, Issue 1, 2004, Pages 195-206

  Lozin, V ^a   Rautenbach, D ^b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

Band width; Clique width; Forbidden induced subgraph; Hereditary class; Tree width

Indexed keywords

CLIQUE-WIDTH; FORBIDDEN INDUCED SUBGRAPHS; HEREDITARY CLASS; TREE-WIDTH;

ALGORITHMS; BANDWIDTH; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; TREES (MATHEMATICS);

GRAPH THEORY;

EID: 14644433034     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480102419755     Document Type: Article

References (18)

1. H. L. BODLAENDBR, A linear-time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput., 25 (1996), pp. 1305-1317.
2. H. L. BODLAENDER, Treewidth: Algorithmic techniques and results, in Mathematical Foundations of Computer Science, Lecture Notes in Comput. Sci. 1295, Springer-Verlag, Berlin, 1997, pp. 19-36.
3. R. BOLIAC AND V. LOZIN, Independent domination infinitely defined classes of graphs, Theoret. Comput. Sci., 301 (2003), pp. 271-284.
4. A. BRANDSTÄDT AND V. V. LOZIN, On the linear structure and clique-width of bipartite permutation graphs, Ars Combin., 67 (2003), pp. 273-281.
5. Y. COLIN DE VERDIERE, Multiplicities of eigenvalues and tree-width of graphs, J. Combin. Theory Ser. B, 74 (1998), pp. 121-146.
6. D. G. CORNEIL, S. OLARIU, AND L. STEWART, Asteroidal triple-free graphs, SIAM J. Discrete Math., 10 (1997), pp. 399-430.
7. B. COURCELLE, The monadic second-order logic of graphs. III. Tree-decompositions, minors and complexity issues, RAIRO Inform. Théor. Appl., 26 (1992), pp. 257-286.
8. B. COURCELLE, J. ENGELFRIET, AND G. ROZENBERG, Handle-rewriting hypergraph grammars, J. Comput. System Sci., 46 (1993), pp. 218-270.
9. B. COURCELLE AND S. OLARIU, Upper bounds to the clique-width of a graph, Discrete Appl. Math., 101 (2000), pp. 77-114.
10. B. COURCELLE, J. A. MAKOWSKY, AND U. ROTICS, Linear time solvable optimization problems on graphs of bounded clique-width, Theory Comput. Syst., 33 (2000), pp. 125-150.
11. B. COURCELLE, J. A. MAKOWSKY, AND U. ROTICS, On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic, Discrete Appl. Math., 108 (2001), pp. 23-52.
12. J. DÍAZ, J. PETIT, AND M. J. SERNA, A survey of graph layout problems, ACM Computing Surveys, 34 (2002), pp. 313-356.
13. M. C. GOLUMBIC AND U. ROTICS, On the clique-width of some perfect graph classes, Internat. J. Found. Comput. Sci., 11 (2000), pp. 423-443.
14. L. PERKOVIĆ AND B. REED, An improved algorithm for finding tree decompositions of small width, Internat. J. Found. Comput. Sci., 11 (2000), pp. 365-371.
15. S. RAMACHANDRAMURTHI, The structure and number of obstructions to treewidth, SIAM J. Discrete Math., 10 (1997), pp. 146-157.
16. B. REED, Tree width and tangles: A new connectivity measure and some applications, in Surveys in Combinatorics, London Math. Soc. Lecture Note Ser. 241, Cambridge University Press, Cambridge, UK, 1997, pp. 87-162.
17. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. II. Algorithmic aspects of tree-width, J. Algorithms, 7 (1986), pp. 309-322.
18. N. ROBERTSON, P. D. SEYMOUR, AND R. THOMAS, Quickly excluding a planar graph, J. Combin. Theory Ser. B, 62 (1994), pp. 323-348.