A shorter proof of the graph minor algorithm - The unique linkage theorem

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2010, Pages 687-694

  Kawarabayashi, Ken Ichi ^a   Wollan, Paul ^b  

^a NATIONAL INSTITUTE OF INFORMATICS   (Japan)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

disjoint paths problem; graph minors; linkages

Indexed keywords

DISJOINT PATHS PROBLEM; EDGE-DISJOINT PATHS; GRAPH MINORS; POLYNOMIAL-TIME ALGORITHMS; PROOF OF CORRECTNESS; STRUCTURE OF GRAPH;

ALGORITHMS; POLYNOMIAL APPROXIMATION;

THEOREM PROVING;

EID: 77954728806     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1806689.1806784     Document Type: Conference Paper

References (36)

1. S. Arnborg and A. Proskurowski, Linear time algorithms for NP-hard problems restricted to partial k-trees, Discrete Appl. Math. 23 (1989), 11-24.
2. H. L. Bodlaender, A linear-time algorithm for finding tree-decomposition of small treewidth, SIAM J. Comput. 25 (1996), 1305-1317.
3. H. L. Bodlaender, F. Fomin, D. Lokshtanov, E. Penninkx, S. Saurabh and D. Thilikos, (Meta) kernelization, to appear in 50th Annual Symposium on Foundations of Computer Science (FOCS 2009).
4. E. D. Demaine, F. Fomin, M. Hajiaghayi, and D. Thilikos, Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs, J. ACM 52 (2005), 1-29.
5. E. D. Demaine, M. Hajiaghayi, and K. Kawarabayashi, Algorithmic graph minor theory: Decomposition, approximation and coloring, Proc. 46th Annual Symposium on Foundations of Computer Science (FOCS'05), 637-646, (2005).
6. E. D. Demaine, M. Hajiaghayi, and B. Mohar, Approximation algorithms via contraction decomposition, Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'07), 278-287, (2007).
7. R. Diestel, Graph Theory, 3rd Edition, Springer, 2005.
8. R.G. Downey and M.R. Fellows, Parameterized complexity, Springer-Verlag, 1999.
9. Z. Dvorak, D. Kral and R. Thomas, Coloring triangle-free graphs on surfaces, ACM-SIAM Symposium on Discrete Algorithms (SODA), 2009, 120-129.
10. M.R. Fellows and M. A. Langston, Nonconstructive tools for proving polynomial-time decidability, J. ACM 35, (1988), 727-739.
11. A. Frank, Packing paths, cuts and circuits - a survey, in Paths, Flows and VLSI-Layout, B. Korte, L. Lovász, H. J. Promel and A. Schrijver (Eds.), Springer-Verlag, Berlin, 1990, 49-100.
12. M. Grohe, Local tree-width, excluded minors, and approximation algorithms. Combinatorica 23, (2003), 613-632.
13. R. M. Karp, On the computational complexity of combinatorial problems, Networks 5 (1975), 45-68.
14. K. Kawarabayashi, Planarity allowing few error vertices in linear time, 50th Annual Symposium on Foundations of Computer Science (FOCS 2009), 639-648, (2009).
15. K. Kawarabayashi and B. Reed, Computing crossing number in linear time, Proc. 39th ACM Symposium on Theory of Computing (STOC'07), 382-390, (2007).
16. K. Kawarabayashi and B. Mohar, Graph and Map Isomorphism and all polyhedral embeddings in linear time, Proc. 40th ACM Symposium on Theory of Computing (STOC'08), 471-480, (2008).
17. K. Kawarabayashi, B. Mohar and B. Reed, A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of bounded tree-width graphs, Proc. 49th Annual Symposium on Foundations of Computer Science (FOCS'08), 771-780, (2008).
18. K. Kawarabayashi, Y. Kobayashi and B. Reed, The disjoint paths problem in quaratic time, submitted.
19. K. Kawarabayashi and Y. Kobayashi, The edge-disjoint paths problem for 4-edge-connected graphs and Eulerian graphs, ACM-SIAM Symposium on Discrete Algorithms (SODA), 345-353, (2010).
20. Y. Kobayashi and K. Kawarabayashi, Algorithms for finding an induced cycle in planar graphs and bounded genus graphs, ACM-SIAM Symposium on Discrete Algorithms (SODA), 1146-1155, (2009).
21. L. Lovász, in Combinatorics, Proc. Fifith Hungarian Combin. Colloq., Keszthely, 1976, Vol. II, p.1208, North-Holland, Amsterdam, 1978.
22. J. F. Lynch, The equivalence of theorem proving and the interconnection problem, ACM SIGDA Newsletter 5 (1975), 31-65.
23. D. Marx and I. Schlotter, Obtaining a planar graph by vertex deletion, Proc. the 33rd Workshop on Graph-Theoretic Concepts in Computer Scienece, 292-303, (2007).
24. M. Milgram and P. Ungar, Amer. Math. Monthly, 85, (1978), 664-668.
25. B. Reed, Tree width and tangles: a new connectivity measure and some applications, in "Surveys in Combinatorics, 1997 (London)", London Math. Soc. Lecture Note Ser. 241, Cambridge Univ. Press, Cambridge, 87-162, (1997).
26. B. Reed, N. Robertson, A. Schrijver and P. D. Seymour, Finding disjoint trees in planar graphs in linear time, Contemp. Math., 147, Amer. Math. Soc., Providenc, RI, 1993, 295-301.
27. N. Robertson and P. D. Seymour, An outline of a disjoint paths algorithm, in Paths, Flows, and VLSI-Layout, B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver (Eds.), Springer-Verlag, Berlin, 1990, 267-292.
28. N. Robertson and P. D. Seymour, Graph minors. VI. Disjoint paths across a disk, J. Combin. Theory Ser. B, 41 (1986), 115-138.
29. N. Robertson and P. D. Seymour, Graph minors. VII. Disjoint paths on a surface, J. Combin. Theory Ser. B, 45 (1988), 212-254.
30. N. Robertson and P. D. Seymour, Graph minors IX. Disjoint crossed paths, J. Combin. Theory Ser. B, 49 (1990), 40-77.
31. N. Robertson and P. D. Seymour, Graph minors. XIII. The disjoint paths problem, J. Combin. Theory Ser. B 63 (1995), 65-110.
32. N. Robertson and P. D. Seymour, Graph minors. XV. Giant Steps, J. Combin. Theory Ser. B 68 (1996), 112-148.
33. N. Robertson and P. D. Seymour, Graph minors. XVI. Excluding a non-planar graph, J. Combin. Theory Ser. B 89 (2003), 43-76.
34. N. Robertson and P. D. Seymour, Graph minors. XXI. Graphs with unique linkages, J. Combin. Theory Ser. B 99 (2009), 583-616.
35. N. Robertson and P. D. Seymour, Graph minors. XXII. Irrelevant vertices in linkage problems, to appear in J. Combin. Theory Ser. B.
36. A. Schrijver, Combinatorial Optimization: Polyhedra and Efficiency, number 24 in Algorithm and Combinatorics, Springer Verlag, 2003.