Hard enumeration problems in geometry and combinatorics
SIAM Journal on Algebraic and Discrete Methods
On the cover polynomial of a digraph
Journal of Combinatorial Theory Series B
Regular Article: The Cycle-Path Indicator Polynomial of a Digraph
Advances in Applied Mathematics
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
A Tutte Polynomial for Coloured Graphs
Combinatorics, Probability and Computing
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Computational Complexity of Tutte Invariants for Planar Graphs
SIAM Journal on Computing
Inapproximability of the Tutte polynomial
Information and Computation
Computing the Tutte Polynomial in Vertex-Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Theory of Computing Systems
A Most General Edge Elimination Polynomial
Graph-Theoretic Concepts in Computer Science
A Most General Edge Elimination Polynomial - Thickening of Edges
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
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
Complexity of the cover polynomial
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Weighted counting of k-matchings is #w[1]-hard
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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The cover polynomials are bivariate graph polynomials that can be defined as weighted sums over all path-cycle covers of a graph. In [3], a dichotomy result for the cover polynomials was proven, establishing that their evaluation is #P-hard everywhere but at a finite set of points, where evaluation is in FP. In this paper, we show that almost the same dichotomy holds when restricting the evaluation to planar graphs. We even provide hardness results for planar DAGs of bounded degree. For particular subclasses of planar graphs of bounded degree and for variants thereof, we also provide algorithms that allow for polynomial-time evaluation of the cover polynomials at certain new points by utilizing Valiant's holographic framework.