On the colored Tutte polynomial of a graph of bounded treewidth

Discrete Applied Mathematics

Volumn 154, Issue 6, 2006, Pages 1032-1036

  Traldi, Lorenzo ^a  

^a LAFAYETTE COLLEGE   (United States)

Author keywords

Colored Tutte polynomial; k sum; Splitting formula; Treewidth

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; GRAPH THEORY; TREES (MATHEMATICS);

COLORED TUTTE POLYNOMIAL; K-SUM; SPLITTING FORMULA; TREEWIDTH;

POLYNOMIALS;

EID: 33644772216     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.09.013     Document Type: Article

References (24)

1. A. Andrzejak Splitting formulas for Tutte polynomials J. Combin. Theory Ser. B 70 1997 346 366
2. A. Andrzejak An algorithm for the Tutte polynomials of graphs of bounded treewidth Discrete Math. 190 1998 39 54
3. H.L. Bodlaender A linear time algorithm for finding tree-decompositions of small treewidth SIAM J. Comput. 25 1996 1305 1317
4. H.L. Bodlaender, T. Hagerup, Parallel algorithms with optimal speedup for bounded treewidth, Automata, Languages and Programming (Szeged, 1995), Lecture Notes in Computer Science, vol. 944, Springer, Berlin, 1995, pp. 268-279.
5. B. Bollobás Modern Graph Theory 1998 Springer New York
6. B. Bollobás, and O. Riordan A Tutte polynomial for colored graphs Comb. Probab. Comput. 8 1999 45 93
7. J.E. Bonin, and A. de Mier Tutte polynomials of generalized parallel connections Adv. in Appl. Math. 32 2004 31 43
8. T. Brylawski A decomposition for combinatorial geometries Trans. Amer. Math. Soc. 171 1972 235 282
9. J.A. Ellis-Monaghan, L. Traldi, Parametrized Tutte polynomials of graphs and matroids, Comb. Probab. Comput., to appear.
10. F. Jaeger, D. Vertigan, and D.J.A. Welsh On the computational complexity of the Jones and Tutte polynomials Math. Proc. Cambridge Philos. Soc. 108 1990 35 53
11. J.A. Makowsky, Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width (extended abstract), Proceedings of the Twelth Annual ACM-SIAM Symposium on Discrete Algorithms (Washington, DC, 2001), SIAM, Philadelphia, PA, 2001, pp. 487-495.
12. J.A. Makowsky Algorithmic aspects of the Feferman-Vaught theorem Ann. Pure Appl. Logic 126 2004 159 213
13. J.A. Makowsky Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width Discrete Appl. Math. 145 2005 276 290
14. S. Negami Polynomial invariants of graphs Trans. Amer. Math. Soc. 299 1987 601 622
15. S.D. Noble Evaluating the Tutte polynomial for graphs of bounded treewidth Comb. Probab. Comput. 7 1998 307 321
16. J.G. Oxley A note on Negami's polynomial invariants for graphs Discrete Math. 76 1989 279 281
17. J.G. Oxley Matroid Theory 1992 Oxford University Press Oxford
18. N. Robertson, and P.D. Seymour Graph minors. I. Excluding a forest J. Combin. Theory Ser. B 35 1983 39 61
19. N. Robertson, and P.D. Seymour Graph minors. III. Planar tree-width J. Combin. Theory Ser. B 36 1984 49 64
20. N. Robertson, and P.D. Seymour Graph minors. II. Algorithmic aspects of tree-width J. Algorithms 7 1986 309 322
21. D.J.A. Welsh Complexity: Knots, Colorings and Counting 1995 Cambridge University Press Cambridge
22. N. White Theory of Matroids 1986 Cambridge University Press Cambridge
23. N. White Matroid Applications 1992 Cambridge University Press Cambridge
24. T. Zaslavsky Strong Tutte functions of matroids and graphs Trans. Amer. Math. Soc. 334 1992 317 347