Boolean-width of graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5917 LNCS, Issue , 2009, Pages 61-74

  Bui Xuan, B M ^a   Telle, J A ^a   Vatshelle, M ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CLIQUE-WIDTH; DECOMPOSITION TREES; DIVIDE-AND-CONQUER APPROACH; GRAPH PARAMETERS; GRAPH PROBLEMS; INDEPENDENT DOMINATING SET; MAXIMUM INDEPENDENT SETS; MINIMUM DOMINATING SET; N-VERTEX GRAPH; RANK-WIDTH; RUNTIMES; TREE-WIDTH;

SET THEORY; WIRELESS TELECOMMUNICATION SYSTEMS;

GRAPH THEORY;

EID: 72249118700     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-11269-0_5     Document Type: Conference Paper

References (23)

1. Adler, I., Vatshelle, M.: Personal communication
2. Bodlaender, H., Koster, A.: Treewidth Computations I Upper Bounds. Technical Report UU-CS-2008-032, Department of Information and Computing Sciences, Utrecht University (2008)
3. Brandstaedt, A., Lozin, V.V.: On the linear structure and clique-width of bipartite permutation graphs. Ars Combinatoria 67, 719-734 (2003)
4. Bui-Xuan, B.-M., Telle, J.A., Vatshelle, M.: Fast FPT algorithms for vertex subset and vertex partitioning problems using neighborhood unions, http://arxiv.org/abs/0903.4796+
5. Bui-Xuan, B.-M., Telle, J.A., Vatshelle, M.: H-join decomposable graphs and algorithms with runtime single exponential in rankwidth. To appear in DAM: special issue of GROW, http://www.ii.uib.no/~telle/bib/BTV.pdf
6. Corneil, D., Rotics, U.: On the relationship between clique-width and treewidth. SIAM Journal on Computing 34(4), 825-847 (2005)
7. Damm, C., Kim, K.H., Roush, F.W.: On covering and rank problems for boolean matrices and their applications. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, pp. 123-133. Springer, Heidelberg (1999)
8. Dorn, F.: Dynamic programming and fast matrix multiplication. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 280-291. Springer, Heidelberg (2006)
9. Ganian, R., Hliněný, P.: On Parse Trees and Myhill-Nerode-type Tools for handling Graphs of Bounded Rank-width (submitted manuscript), http://www.fi.muni.cz/~hlineny/Research/papers/MNtools+dam3.pdf
10. Geelen, J., Gerards, A., Whittle, G.: Branch-width and well-quasi-ordering in matroids and graphs. Journal of Combinatorial Theory, Series B 84(2), 270-290 (2002)
11. Hliněný, P., Oum, S.: Finding branch-decompositions and rank-decompositions. SIAM Journal on Computing 38(3), 1012-1032 (2008); Abstract at ESA 2007.
12. Hliněný, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. The Computer Journal 51(3), 326-362 (2008)
13. Hsu, W.-L.: Decomposition of perfect graphs. Journal of Combinatorial Theory, Series B 43(1), 70-94 (1987)
14. Jelínek, V.: The rank-width of the square grid. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds.) WG 2008. LNCS, vol. 5344, pp. 230-239. Springer, Heidelberg (2008)
15. Kim, K.H.: Boolean matrix theory and its applications. Marcel Dekker, New York (1982)
16. Kobler, D., Rotics, U.: Edge dominating set and colorings on graphs with fixed clique-width. Discrete Applied Mathematics 126(2-3), 197-221 (2003); Abstract at SODA 2001
17. Nguyen, H.X., Thiran, P.: Active measurement for multiple link failures diagnosis in IP networks. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 185-194. Springer, Heidelberg (2004)
18. Oum, S.: Graphs of Bounded Rank-width. PhD thesis, Princeton University (2005)
19. Oum, S.: Rank-width is less than or equal to branch-width. Journal of Graph Theory 57(3), 239-244 (2008)
20. Oum, S., Seymour, P.: Approximating clique-width and branch-width. Journal of Combinatorial Theory, Series B 96(4), 514-528 (2006)
21. Pattison, P., Breiger, R.: Lattices and dimensional representations: matrix decompositions and ordering structures. Social Networks 24(4), 423-444 (2002)
22. Robertson, N., Seymour, P.: Graph minors. X. Obstructions to tree-decomposition. Journal of Combinatorial Theory, Series B 52(2), 153-190 (1991)
23. Rooij, J., Bodlaender, H., Rossmanith, P.: Dynamic programming on tree decompositions using generalised fast subset convolution. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 566-577. Springer, Heidelberg (2009)