Enumerative combinatorics
Map coloring and the vector cross product
Journal of Combinatorial Theory Series B
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
A note on graph colorings and graph polynomials
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series A
Support Weight Enumerators and Coset Weight Distributions of Isodual Codes
Designs, Codes and Cryptography
Some new evaluations of the Tutte polynomial
Journal of Combinatorial Theory Series B
Some probabilistic restatements of the Four Color Conjecture
Journal of Graph Theory
Evaluations of Graph Polynomials
Graph-Theoretic Concepts in Computer Science
Connection Matrices for MSOL-Definable Structural Invariants
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
One more probabilistic reformulation of the four colour conjecture
Combinatorics, Probability and Computing
Congruence conditions, parcels, and Tutte polynomials of graphs and matroids
Journal of Combinatorial Theory Series B
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Identities obtained by elementary finite Fourier analysis are used to derive a variety of evaluations of the Tutte polynomial of a graph G at certain points (a,b) where (a-1)(b-1)@?{2,4}. These evaluations are expressed in terms of eulerian subgraphs of G and the size of subgraphs modulo 2,3,4 or 6. In particular, a graph is found to have a nowhere-zero 4-flow if and only if there is a correlation between the event that three subgraphs A,B,C chosen uniformly at random have pairwise eulerian symmetric differences and the event that @?|A|+|B|+|C|3@? is even. Some further evaluations of the Tutte polynomial at points (a,b) where (a-1)(b-1)=3 are also given that illustrate the unifying power of the methods used. The connection between results of Matiyasevich, Alon and Tarsi and Onn is highlighted by indicating how they may all be derived by the techniques adopted in this paper.