The search for chromatically unique graphs—II
CPRT '94 Proceedings of the conference on Chromatic polynomials and related topics
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Contraction-deletion invariants for graphs
Journal of Combinatorial Theory Series B
Locally grid graphs: classification and Tutte uniqueness
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Graphs determined by polynomial invariants
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
A Tutte Polynomial for Coloured Graphs
Combinatorics, Probability and Computing
On Graphs Determined by Their Tutte Polynomials
Graphs and Combinatorics
The rank of connection matrices and the dimension of graph algebras
European Journal of Combinatorics
On chromatic and flow polynomial unique graphs
Discrete Applied Mathematics
The bivariate Ising polynomial of a graph
Discrete Applied Mathematics
Homomorphisms and polynomial invariants of graphs
European Journal of Combinatorics
Note: Dual graph homomorphism functions
Journal of Combinatorial Theory Series A
An extension of the bivariate chromatic polynomial
European Journal of Combinatorics
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We introduce a new property of graphs called 'q-state Potts uniqueness' and relate it to chromatic and Tutte uniqueness, and also to 'chromatic-flow uniqueness', recently studied by Duan, Wu and Yu. We establish for which edge-weighted graphs H homomorphism functions from multigraphs G to H are specializations of the Tutte polynomial of G, in particular answering a question of Freedman, Lovasz and Schrijver. We also determine for which edge-weighted graphs H homomorphism functions from multigraphs G to H are specializations of the 'edge elimination polynomial' of Averbouch, Godlin and Makowsky and the 'induced subgraph polynomial' of Tittmann, Averbouch and Makowsky. Unifying the study of these and related problems is the notion of the left and right homomorphism profiles of a graph.