Parametrized Tutte polynomials of graphs and matroids

Combinatorics Probability and Computing

Volumn 15, Issue 6, 2006, Pages 835-854

  Ellis Monaghan, Joanna A ^a   Traldi, Lorenzo ^b  

^a SAINT MICHAEL'S COLLEGE   (United States)

^b LAFAYETTE COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; MATRIX ALGEBRA; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

CORANK NULLITY FORMULAS; PARAMETRIZED CONTRACTION DELETION FUNCTIONS; TUTTE POLYNOMIALS;

GRAPH THEORY;

EID: 33750375727     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548306007656     Document Type: Article

References (19)

1. Bollobás, B. (1998) Modern Graph Theory, Springer, New York.
2. Bollobás, B. and Riordan, O. (1999) A Tutte polynomial for coloured graphs. Combin. Probab. Comput. 8 45-93.
3. Brylawski, T. (1971) A combinatorial model for series-parallel networks. Trans. Amer. Math. Soc. 154 1-22.
4. Essam, J. W. (1971) Graph theory and statistical physics. Discrete Math. 1 83-112.
5. Fortuin, C. M. and Kasteleyn, P. W. (1972) On the random-cluster model I: Introduction and relation to other models. Physica 57 536-564.
6. Gordon, G. and Traldi, L. (1990) Generalized activities and the Tutte polynomial. Discrete Math. 85 167-176.
7. Oxley, J. G. (1992) Matroid Theory, Oxford University Press, Oxford.
8. Oxley, J. G. and Welsh, D. J. A. (1992) Tutte polynomials computable in polynomial time. Discrete Math. 109 185-192.
9. Read, R. C. and Whitehead Jr., E. G. (1999) Chromatic polynomials of homeomorphism classes of graphs. Discrete Math. 204 337-356.
10. Traldi, L. (1989) A dichromatic polynomial for weighted graphs and link polynomials. Proc. Amer. Math. Soc. 106 279-286.
11. Traldi, L. (2004) A subset expansion of the coloured Tutte polynomial. Combin. Probab. Comput. 13 269-275.
12. Traldi, L. (2005) Generalized activities and reliability. J. Combin. Math. Combin. Comp. 15 17-32.
13. Traldi, L. (2005) Parallel connections and the colored Tutte polynomial. Discrete Math. 290 291-299.
14. Tutte, W. T. (1984) Graph Theory, Cambridge University Press, Cambridge.
15. Welsh, D. J. A. (1995) Complexity: Knots, Colourings and Counting, Cambridge University Press, Cambridge.
16. White, N., ed., (1986) Theory of Matroids, Cambridge University Press, Cambridge.
17. White, N., ed., (1992) Matroid Applications, Cambridge University Press, Cambridge.
18. Woodall, D. R. (2002) Tutte polynomial expansions for 2-separable graphs. Discrete Math. 247 201-213.
19. Zaslavsky, T. (1992) Strong Tutte functions of matroids and graphs. Trans. Amer. Math. Soc. 334 317-347.