Tight bounds for linkages in planar graphs

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

Volumn 6755 LNCS, Issue PART 1, 2011, Pages 110-121

  Adler, Isolde ^a   Kolliopoulos, Stavros G ^b   Krause, Philipp Klaus ^a   Lokshtanov, Daniel ^c   Saurabh, Saket ^d   Thilikos, Dimitrios ^b  

^a GOETHE UNIVERSITY   (Germany)

^b UNIVERSITY OF ATHENS   (Greece)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL PROPERTIES; GENERAL GRAPH; GRAPH G; PARAMETER DEPENDENCE; PLANAR GRAPH; RUNNING TIME; TIGHT BOUND; TREE-WIDTH; VERTEX DISJOINT PATHS;

ALGORITHMS; GRAPHIC METHODS; THEOREM PROVING;

GRAPH THEORY;

EID: 79959986071     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-22006-7_10     Document Type: Conference Paper

References (23)

1. Adler, I., Kolliopoulos, S.G., Thilikos, D.: Planar disjoint paths completion. Submitted for publication (2011)
2. Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybernet. 11(1-2), 1-21 (1993)
3. Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: LICS 2007, pp. 270-279. IEEE Computer Society, Los Alamitos (2007)
4. Dawar, A., Kreutzer, S.: Domination problems in nowhere-dense classes. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009), pp. 157-168 (2009)
5. Diestel, R.: Graph Theory. Springer, Heidelberg (2005)
6. Ellis, J., Warren, R.: Lower Bounds on the Pathwidth of some Grid-like Graphs. Discrete Applied Mathematics 156(5), 545-555 (2008)
7. Golovach, P.A., Kaminski, M., Paulusma, D., Thilikos, D.M.: Induced packing of odd cycles in a planar graph. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 514-523. Springer, Heidelberg (2009)
8. Kawarabayashi, K.-i., Kobayashi, Y.: The induced disjoint paths problem. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 47-61. Springer, Heidelberg (2008)
9. Kawarabayashi, K.-i., Reed, B.: Odd cycle packing. In: Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC 2010), pp. 695-704. ACM, New York (2010)
10. Kawarabayashi, K.-i., Wollan, P.: A shorter proof of the graph minor algorithm: the unique linkage theorem. In: Proc. of the 42nd annual ACM Symposium on Theory of Computing (STOC 2010), pp. 687-694 (2010)
11. Kobayashi, Y., Kawarabayashi, K.-i.: Algorithms for finding an induced cycle in planar graphs and bounded genus graphs. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), pp. 1146-1155. ACM-SIAM (2009)
12. Kramer, M.R., van Leeuven, J.: The complexity of wire-routing and finding minimum area layouts for arbitrary VLSI circuits. Advances in Comp. Research 2, 129-146 (1984)
13. Lokshtanov, D., Marx, D., Saurabh, S.: Slightly superexponential parameterized problems. In: 22st ACM-SIAM Symposium on Discrete Algorithms (SODA 2011), pp. 760-776 (2011)
14. Lynch, J.F.: The equivalence of theorem proving and the interconnection problem. ACM SIGDA Newsletter 5, 31-36 (1975)
15. Middendorf, M., Pfeiffer, F.: On the complexity of the disjoint paths problem. Combinatorica 13(1), 97-107 (1993)
16. Reed, B., Robertson, N., Schrijver, A., Seymour, P.D.: Finding dsjoint trees in planar graphs in linear time. In: Robertson, N., Seymour, P.D. (eds.) Graph Structure Theory. Contemporary Mathematics, vol. 147, pp. 295-302. American Mathematical Society, Providence (1991)
17. Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B 63(1), 65-110 (1995)
18. Robertson, N., Seymour, P.: Graph minors. XXI. Graphs with unique linkages. J. Combin. Theory Ser. B 99(3), 583-616 (2009)
19. Robertson, N., Seymour, P.D.: Graph Minors. XXII. Irrelevant vertices in linkage problems. Journal of Combinatorial Theory, Series B (to appear)
20. Robertson, N., Seymour, P.D.: Graph minors. XXI. Graphs with unique linkages. Journal of Combinatorial Theory, Series B 99(3), 583-616 (2009)
21. Schrijver, A.: Finding k disjoint paths in a directed planar graph. SIAM J. Comput. 23(4), 780-788 (1994)
22. Schrijver, A.: Combinatorial optimization. Polyhedra and efficiency, vol. A. Springer, Berlin (2003)
23. Vygen, J.: NP-completeness of some edge-disjoint paths problems. Discrete Appl. Math. 61(1), 83-90 (1995)