Evaluating a weighted graph polynomial for graphs of bounded tree-width

Electronic Journal of Combinatorics

Volumn 16, Issue 1, 2009, Pages

  Noble, S D ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

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[No Author keywords available]

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EID: 67649908566     PISSN: None     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/153     Document Type: Article

References (29)

1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading Massachusetts, 1974.
2. A. Andrzejak. A polynomial-time algorithm for computation of the Tutte polynomials of graphs of bounded treewidth. Discrete Mathematics, 190:39-54, 1998.
3. S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM Journal of Algebraic and Discrete Methods, 8:277-284, 1987.
4. S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics, 23:11-24, 1989.
5. H. L. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11:1-21, 1993.
6. H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing, 25:1305-1317, 1996.
7. B. Bollob'as and O. Riordan. A Tutte polynomial for coloured graphs. Combinatorics, Probability and Computing, 8:45-94, 1999.
8. T. H. Brylawski and J. G. Oxley. The Tutte polynomial and its applications. In N. White, editor, Matroid applications, pages 123-225. Cambridge University Press, Cambridge, 1992.
9. S. V. Chmutov, S. V. Duzhin, and S. K. Lando. Vassiliev knot invariants: I. Introduction. Advances in Soviet Mathematics, 21:117-126, 1994.
10. S. V. Chmutov, S. V. Duzhin, and S. K. Lando. Vassiliev knot invariants: II. Intersection graph for trees. Advances in Soviet Mathematics, 21:127-134, 1994.
11. S. V. Chmutov, S. V. Duzhin, and S. K. Lando. Vassiliev knot invariants: III. Forest algebra and weighted graphs. Advances in Soviet Mathematics, 21:135-145, 1994.
12. J. Edmonds. Systems of distinct representatives and linear algebra. Journal of Research of the National Bureau of Standards Section B, 71B:241-245, 1967.
13. G. E. Farr. A correlation inequality involving stable sets and chromatic polynomials. Journal of Combinatorial Theory Series B, 58:14-21, 1993.
14. E. J. Farrell. On a general class of graph polynomials. Journal of Combinatorial Theory Series B, 26:111-122, 1979.
15. P. Hliňen'y. The Tutte polynomial for matroids of bounded branch-width. Combina- torics, Probability and Computing, 15:397-409, 2006.
16. F. Jaeger, D. L. Vertigan, and D. J. A. Welsh. On the computational complexity of the Jones and Tutte polynomials. Mathematical Proceedings of the Cambridge Philosophical Society, 108:35-53, 1990.
17. J. A. Makowsky. Coloured Tutte polynomials and Kaufmann brackets for graphs of bounded tree width. Discrete Applied Mathematics, 145:276-290, 2005.
18. J. A. Makowsky. Personal Communication, 2008.
19. J. A. Makowsky and J. P. Marĩno. Farrell polynomials on graphs of bounded tree width. Advances in Applied Mathematics, 30:160-176, 2003. Special issue of FPSAC' 01 papers.
20. S. D. Noble. Evaluating the Tutte polynomial for graphs of bounded tree-width. Combinatorics, Probability and Computing, 7:307-321, 1998.
21. S. D. Noble. Complexity of graph polynomials. In G. Grimmett and C. J. H. Mc- Diarmid, editors, Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh. Oxford University Press, Oxford, 2007.
22. S. D. Noble and D. J. A. Welsh. A weighted graph polynomial from chromatic invariants of knots. Annales de l'Institut Fourier, 49:1057-1087, 1999.
23. J. G. Oxley and G. P. Whittle. A characterization of Tutte invariants of 2- polymatroids. Journal of Combinatorial Theory Series B, 59:210-244, 1993.
24. N. Robertson and P. D. Seymour. Graph minors II. Algorithmic aspects of tree-width. Journal of Algorithms, 7:309-322, 1986.
25. N. Robertson and P. D. Seymour. Graph minors IV. Tree-width and well-quasiordering. Journal of Combinatorial Theory Series B, 48:227-254, 1990.
26. I. Sarmiento. The polychromate and a chord diagram polynomial. Annals of Com- binatorics, 4:227-236, 2000.
27. R. P. Stanley. A symmetric function generalisation of the chromatic polynomial of a graph. Advances in Mathematics, 111:166-194, 1995.
28. D. L. Vertigan and D. J. A.Welsh. The computational complexity of the Tutte plane: the bipartite case. Combinatorics Probability and Computing, 1:181-187, 1992.
29. D. J. A. Welsh. Complexity : Knots, Colourings, and Counting. Number 186 in London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1993.