Results 131 to 140 of about 156 (150)
Aequationes Mathematicae, 1969 $q$-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a "classical" matroid. Tutte polynomials $\tau(x,y)$ of matroids are calculated either by recursion over deletion/contraction of single elements, by an enumeration of bases with respect to internal/external activities, or by substitution $x \to
Henry H Crapo
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Journal of Graph Theory, 1991
AbstractWe define two two‐variable polynomials for rooted trees and one two‐variable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees T1 and T2 are ...
Sharad Chaudhary, Gary Gordon
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AbstractWe define two two‐variable polynomials for rooted trees and one two‐variable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees T1 and T2 are ...
Sharad Chaudhary, Gary Gordon
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ACM Transactions on Mathematical Software, 2010
The Tutte polynomial of a graph, also known as the partition function of the q -state Potts model is a 2-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial ...
Gary Haggard +2 more
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The Tutte polynomial of a graph, also known as the partition function of the q -state Potts model is a 2-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial ...
Gary Haggard +2 more
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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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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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On Graphs Determined by Their Tutte Polynomials
Graphs and Combinatorics, 2004zbMATH 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, 2020The 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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Chip firing and the tutte polynomial
Annals of Combinatorics, 1997This 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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The Potts model and the Tutte polynomial
Journal of Mathematical Physics, 2000This 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, 1999We 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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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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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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