Results 131 to 140 of about 495 (157)

Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width

Discrete Applied Mathematics, 2005
Tutte polynomials are important graph invariants with rich applications in combinatorics, topology, knot theory, coding theory and even physics. The Tutte polynomial T(G,X,Y) is a polynomial in Z[X,Y] which depends on a graph G.
Johann A Makowsky
exaly   +2 more sources

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The Tutte polynomial

Random Structures and Algorithms, 1999
The author presents some recent evaluations of the Tutte polynomial in terms of coloring and flows in random graphs, lattice point enumeration, and chip firing games. He then considers some complexity issues, in particular, the existence of fully polynomial randomized approximation schemes for evaluating the Tutte polynomial.
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Tutte polynomials for counting and classifying orbits

Discrete Mathematics, 2010
Given a graph Γ and an automorphism group G≤Aut(Γ), we define some polynomials which count and classify the orbits of G on various structures on Γ, as counted by the Tutte polynomial, while also specialising to the Tutte ...
Rudd, Jason D.
exaly   +2 more sources

On Graphs Determined by Their Tutte Polynomials

Graphs and Combinatorics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anna de Mier, Marc Noy
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The Tutte polynomial of ideal arrangements

Discrete Mathematics, Algorithms and Applications, 2020
The Tutte polynomial was originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning subgraphs, and of acyclic orientations.
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The Potts model and the Tutte polynomial

Journal of Mathematical Physics, 2000
This is an invited survey on the relation between the partition function of the Potts model and the Tutte polynomial. On the assumption that the Potts model is more familiar we have concentrated on the latter and its interpretations. In particular we highlight the connections with Abelian sandpiles, counting problems on random graphs, error correcting ...
Welsh, D. J. A., Merino, C.
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A Tutte Polynomial for Coloured Graphs

Combinatorics, Probability and Computing, 1999
We define a polynomial W on graphs with colours on the edges, by generalizing the spanning tree expansion of the Tutte polynomial as far as possible: we give necessary and sufficient conditions on the edge weights for this expansion not to depend on the order used.
Bollobás, Béla, Riordan, Oliver
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The Tutte Polynomial

1998
So far we have encountered several polynomials associated with a graph, including the chromatic polynomial, the characteristic polynomial and the minimal polynomial Our aim in this chapter is to study a polynomial that gives us much more information about our, graph than any of these.
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Chip firing and the tutte polynomial

Annals of Combinatorics, 1997
This paper shows that the generating function of critical configurations of a version of a chip firing game on a graph \(G\) is an evaluation of the Tutte polynomial of \(G\), thus proving a conjecture of Biggs.
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Harmonic Tutte polynomials of matroids

Designs, Codes, and Cryptography, 2023
Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura   +2 more
exaly