Improved data structures for fully dynamic biconnectivity
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The computation of chromatic polynomials
Discrete Mathematics
Computing the Tutte Polynomial of a Graph of Moderate Size
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ®
Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ®
Computing the Tutte Polynomial in Vertex-Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Edge-selection heuristics for computing Tutte polynomials
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
On some Tutte polynomial sequences in the square lattice
Journal of Combinatorial Theory Series B
Is the five-flow conjecture almost false?
Journal of Combinatorial Theory Series B
On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid
Journal of Algebraic Combinatorics: An International Journal
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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 as partial evaluations, and various numerical invariants such as the number of spanning trees as complete evaluations. However despite its ubiquity, there are no widely available effective computational tools able to compute the Tutte polynomial of a general graph of reasonable size. In this article we describe the implementation of a program that exploits isomorphisms in the computation tree to extend the range of graphs for which it is feasible to compute their Tutte polynomials, and we demonstrate the utility of the program by finding counterexamples to a conjecture of Welsh on the location of the real flow roots of a graph.