κ-Gap interval graphs

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

Volumn 7256 LNCS, Issue , 2012, Pages 350-361

  Fomin, Fedor V ^a   Gaspers, Serge ^b   Golovach, Petr ^c   Suchan, Karol ^d,e   Szeider, Stefan ^b   Van Leeuwen, Erik Jan ^a   Vatshelle, Martin ^a   Villanger, Yngve ^a  

^a UNIVERSITY OF BERGEN   (Norway)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^c DURHAM UNIVERSITY   (United Kingdom)

^d UNIVERSIDAD ADOLFO IBÁÑEZ   (Chile)

^e AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMIC PROPERTIES; CLIQUE COVER; COLORING PROBLEMS; DOMINATING SETS; FEEDBACK VERTEX SET; FPT ALGORITHMS; GRAPH PROBLEMS; INDEPENDENT SET; INTERVAL GRAPH; NON-EMPTY INTERSECTIONS; REAL LINE; REPRESENTATION OF A GRAPH; SCALE-UP;

ALGORITHMS; INFORMATION SCIENCE; INTELLIGENT NETWORKS;

GRAPH THEORY;

EID: 84860819332     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-29344-3_30     Document Type: Conference Paper

References (52)

1. Alon, N.: Piercing d-intervals. Discret. Comput. Geom. 19(3), 333-334 (1998)
2. Andreae, T.: On an extremal problem concerning the interval number of a graph. Discrete Appl. Math. 14(1), 1-9 (1986)
3. Andreae, T., Aigner, M.: The total interval number of a graph. J. Comb. Theory Ser. B 46(1), 7-21 (1989)
4. Aumann, Y., Lewenstein, M., Melamud, O., Pinter, R.Y., Yakhini, Z.: Dotted interval graphs and high throughput genotyping. In: SODA 2005, pp. 339-348 (2005)
5. Bafna, V., Narayanan, B.O., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Appl. Math. 71(1-3), 41-53 (1996)
6. Balogh, J., Ochem, P., Pluhár, A.: On the interval number of special graphs. J. Graph Theor. 46(4), 241-253 (2004)
7. Bar-Yehuda, R., Halldórsson, M.M., Naor, J., Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM J. Comput. 36(1), 1-15 (2006)
8. Bar-Yehuda, R., Rawitz, D.: Using fractional primal-dual to schedule split intervals with demands. Discrete Optim. 3(4), 275-287 (2006)
9. Belmonte, R., Vatshelle, M.: Graph Classes with Structured Neighborhoods and Algorithmic Applications. In: Kolman, P., Kratochvíl, J. (eds.) WG 2011. LNCS, vol. 6986, pp. 47-58. Springer, Heidelberg (2011)
10. Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Quimper, C.-G., Walsh, T.: The parameterized complexity of global constraints. In: AAAI 2008, pp. 235-240 (2008)
11. Blin, G., Fertin, G., Vialette, S.: Extracting constrained 2-interval subsets in 2-interval sets. Theor. Comput. Sci. 385(1-3), 241-263 (2007)
12. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209(1-2), 1-45 (1998)
13. Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. J. Comput. System Sci. 13(3), 335-379 (1976)
14. Bui-Xuan, B.-M., Telle, J.A., Vatshelle, M.: Boolean-width of graphs. Theor. Comput. Sci. 412(39), 5187-5204 (2011)
15. Butman, A., Hermelin, D., Lewenstein, M., Rawitz, D.: Optimization problems in multiple-interval graphs. ACM Trans. Algorithms 6(2) (2010)
16. Catlin, P.A.: Supereulerian graphs: A survey. J. Graph Theor. 16(2), 177-196 (1992)
17. Chen, E., Yang, L., Yuan, H.: Improved algorithms for largest cardinality 2-interval pattern problem. J. Comb. Optim. 13(3), 263-275 (2007)
18. Chen, M., Chang, G.J.: Total interval numbers of complete r-partite graphs. Discrete Appl. Math. 122, 83-92 (2002)
19. Courcelle, B.: The monadic second-order logic of graphs III: Tree-decompositions, minor and complexity issues. Rairo-Theor. Inform. Appl. 26, 257-286 (1992)
20. Crochemore,M., Hermelin, D., Landau, G.M., Rawitz, D., Vialette, S.: Approximating the 2-interval pattern problem. Theor. Comput. Sci. 395(2-3), 283-297 (2008)
21. Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer (1999)
22. Erdös, P., West, D.B.: A note on the interval number of a graph. Discrete Math. 55(2), 129-133 (1985)
23. Fellows,M.R., Hermelin, D., Rosamond, F., Vialette, S.: On the parameterized complexity of multiple-interval graph problems. Theor. Comput. Sci. 410, 53-61 (2009)
24. Flum, J., Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series XIV. Springer (2006)
25. Fomin, F.V., Gaspers, S., Golovach, P., Suchan, K., Szeider, S., van Leeuwen, E.J., Vatshelle, M., Villanger, Y.: k-gap interval graphs. arXiv CoRR 1112.3244 (2011)
26. Gambette, P., Vialette, S.: On Restrictions of Balanced 2-Interval Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 55-65. Springer, Heidelberg (2007)
27. Gaspers, S., Szeider, S.: Kernels for global constraints. In: IJCAI 2011, pp. 540-545 (2011)
28. Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Academic Press (1980)
29. Griggs, J.R., West, D.B.: Extremal values of the interval number of a graph. SIAM J. Algebra. Discr. 1(1), 1-7 (1980)
30. Hassin, R., Segev, D.: Rounding to an integral program. Oper. Res. Lett. 36(3), 321-326 (2008)
31. Jansen, B.M.P., Kratsch, S.: Data Reduction for Graph Coloring Problems. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 90-101. Springer, Heidelberg (2011)
32. Jiang, M., Zhang, Y.: Parameterized Complexity in Multiple-interval Graphs: Domination. In: Rossmanith, P. (ed.) IPEC 2011. LNCS, vol. 7112, pp. 27-40. Springer, Heidelberg (2012)
33. Jiang, M., Zhang, Y.: Parameterized Complexity in Multiple-Interval Graphs: Partition, Separation, Irredundancy. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 62-73. Springer, Heidelberg (2011)
34. Kaiser, T.: Transversals of d-intervals. Discret. Comput. Geom. 18(2) (1997)
35. Kloks, T.: Treewidth, Computations and Approximations. LNCS, vol. 842. Springer, Heidelberg (1994)
36. Kostochka, A.V., West, D.B.: Total interval number for graphs with bounded degree. J. Graph Theor. 25(1), 79-84 (1997)
37. Kratzke, T.M., West, D.B.: The total interval number of a graph, I: Fundamental classes. Discrete Math. 118(1-3), 145-156 (1993)
38. Kratzke, T.M., West, D.B.: The total interval number of a graph II: Trees and complexity. SIAM J. Discrete Math. 9(2), 339-348 (1996)
39. Marx, D.: Parameterized coloring problems on chordal graphs. Theor. Comput. Sci. 351(3), 407-424 (2006)
40. Marx, D.: Chordal deletion is fixed-parameter tractable. Algorithmica 57(4), 747-768 (2010)
41. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and Its Applications. Oxford University Press (2006)
42. Raychaudhuri, A.: The total interval number of a tree and the hamiltonian completion number of its line graph. Inform. Process. Lett. 56(6), 299-306 (1995)
43. Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5(2), 266-283 (1976)
44. Scheinerman, E.R., West, D.B.: The interval number of a planar graph: Three intervals suffice. J. Comb. Theory Ser. B 35(3), 224-239 (1983)
45. Spinrad, J.P.: Efficient Graph Representations. Fields Institute Monographs, vol. 19. AMS (2003)
46. Tardos, G.: Transversals of 2-intervals, a topological approach. Combinatorica 15(1), 123-134 (1995)
47. Trotter, W.T., Harary, F.: On double and multiple interval graphs. J. Graph Theor. 3(3), 205-2011 (1979)
48. Tsukiyama, S., Ide, M., Ariyoshi, H., Shirakawa, I.: A new algorithm for generating all the maximal independent sets. SIAM J. Comput. 6(3), 505-517 (1977)
49. Vialette, S.: On the computational complexity of 2-interval pattern matching problems. Theor. Comput. Sci. 312(2-3), 224-239 (2004)
50. Vialette, S.: Two-interval pattern problems. In: Encyclopedia of Algorithms. Springer (2008)
51. West, D.B.: A short proof of the degree bound for interval number. Discrete Math. 73(3), 309-310 (1989)
52. West, D.B., Shmoys, D.B.: Recognizing graphs with fixed interval number is NPcomplete. Discrete Appl. Math. 8, 295-305 (1984)