Hard enumeration problems in geometry and combinatorics
SIAM Journal on Algebraic and Discrete Methods
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Theory of Computing Systems
Complexity of the Bollobás-Riordan polynomial: exceptional points and uniform reductions
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
The enumeration of vertex induced subgraphs with respect to the number of components
European Journal of Combinatorics
The complexity of the cover polynomials for planar graphs of bounded degree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
| Hi-index | 0.00 |
We consider a graph polynomial ξ (G; x, y, z) introduced by Ilia Averbouch,BennyGodlin, and Johann A.Makowsky (2008). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Klaus Dohmen, André Pönitz, and Peter Tittmann (2003). We derive an identity which relates the graph polynomial ξ of a thickened graph (i.e. a graph with each edge replaced by k copies of it) to ξ of the original graph. As a consequence, we observe that at every point (x, y, z), except for points lying within some set of dimension 2, evaluating ξ is #P-hard. Thus, ξ supports Johann A. Makowsky's difficult point conjecture for graph polynomials (2008).