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Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees

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SWAT 88 (SWAT 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 318))

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Abstract

In this paper we show that Graph Isomorphism and Chromatic Index are solvable in polynomial time when restricted to the class of graphs with treewidth ≤k (k a constant) (or equivalently, the class of partial k-trees). Also, we show that there exist algorithms that find tree-decompositions with treewidth ≤k of graphs with treewidth ≤k, in O(n 3) time, (k constant).

Part of this research was done while the author was visiting the Laboratory for Computer Science of the Massachusetts Institute of Technology, with a grant from the Netherlands Organization for the Advancement of Pure Research Z.W.O. Most omitted proofs can be found in the full paper, which is published as technical report at the Dept. for Comp. Science, Univ. of Utrecht.

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References

  1. S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey. BIT, 25:2–23, 1985.

    Google Scholar 

  2. S. Arnborg, D. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth., 8:277–284, 1987.

    Google Scholar 

  3. S. Arnborg, J. Lagergren, and D. Seese. Which problems are easy for tree-decomposable graphs. 1987. Ext. abstract to appear in proc. ICALP 88.

    Google Scholar 

  4. S. Arnborg and A. Proskurowski. Characterization and recognition of partial 3-trees. Siam J. Alg. Disc. Meth., 7:305–314, 1986.

    Google Scholar 

  5. H. L. Bodlaender. Classes of Graphs with Bounded Treewidth. Tech. Rep. RUU-CS-86-22, Dept. Of Comp. Science, University of Utrecht, Utrecht, 1986.

    Google Scholar 

  6. H. L. Bodlaender. Dynamic programming algorithms on graphs with bounded tree-width. Tech. Rep. MIT/LCS/TR-394, Lab. for Comp. Science, M.I.T., 1987. Ext. abstract to appear in proc. ICALP 88.

    Google Scholar 

  7. H. L. Bodlaender. NC-algorithms for graphs with small treewidth. Tech. Rep. RUU-CS-88-4, Dept. of Comp. Science, Univ. of Utrecht, Utrecht, 1988.

    Google Scholar 

  8. B. Courcelle. Recognizability and Second-Order Definability for Sets of Finite Graphs. Preprint, Universite de Bordeaux, Jan. 1987.

    Google Scholar 

  9. M. R. Fellows and M. A. Langston. Nonconstructive tools for proving polynomial-time decidability. 1987. To appear in JACM.

    Google Scholar 

  10. I. Holyer. The NP-completeness of edge-coloring. SIAM J. Comput, 10:718–720, 1981.

    Google Scholar 

  11. J. E. Hopcroft and R. M. Karp. An n 5/2 algorithm for maximum matching in bipartite graphs. SAIM J. on Comput., 225–231, 1975.

    Google Scholar 

  12. D. S. Johnson. The NP-completeness column: an ongoing guide. J. of Algorithms, 6:434–451, 1985.

    Google Scholar 

  13. N. Robertson and P. Seymour. Graph minors. III. Planar tree-width. J. Combin. Theory Series B, 36:49–64, 1984.

    Google Scholar 

  14. N. Robertson and P. Seymour. Graph minors. X. Obstructions to tree-decompositions. 1986. Manuscript.

    Google Scholar 

  15. N. Robertson and P. Seymour. Graph minors. XII. Excluding a non-planar graph. 1986. Manuscript.

    Google Scholar 

  16. N. Robertson and P. Seymour. Graph minors. XIII. The disjoint paths problem. 1986. Manuscript.

    Google Scholar 

  17. P. Scheffler. Linear-time algorithms for NP-complete problems restricted to partial k-trees. Report R-MATH-03/87, Karl-Weierstrass-Institut Für Mathematik, Berlin, GDR, 1987.

    Google Scholar 

  18. M. M. Sysło. NP-complete problems on some tree-structured graphs: a review. In M. Nagl and J. Perl, editors, Proc. WG'83 International Workshop on Graph Theoretic Concepts in Computer Science, pages 342–353, Univ. Verlag Rudolf Trauner, Linz, West Germany, 1983.

    Google Scholar 

  19. J. Valdes, R. Tarjan, and E. L. Lawler. The recognition of series parallel digraphs. SIAM J. Comput., 11:298–313, 1982.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Computer Science, University of Utrecht, P.O. Box 80.012, 3508 TA, Utrecht, the Netherlands

    Hans L. Bodlaender

Authors
  1. Hans L. Bodlaender
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Rolf Karlsson Andrzej Lingas

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© 1988 Springer-Verlag Berlin Heidelberg

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Bodlaender, H.L. (1988). Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_26

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  • DOI: https://doi.org/10.1007/3-540-19487-8_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19487-3

  • Online ISBN: 978-3-540-39288-0

  • eBook Packages: Springer Book Archive

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