Tutte polynomials computable in polynomial time
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
On the complexity of approximating extremal determinants in matrices
Journal of Complexity
The complexities of the coefficients of the Tutte polynomial
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Non-Stanley Bounds for Network Reliability
Journal of Algebraic Combinatorics: An International Journal
Polynomial time randomized approximation schemes for Tutte-Gro¨thendieck invariants: the dense case
Random Structures & Algorithms
On coefficients of the Tutte polynomial
Discrete Mathematics
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
Graph orientations with no sink and an approximation for a hard case of #SAT
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Branch-width and well-quasi-ordering in matroids and graphs
Journal of Combinatorial Theory Series B
On the computational complexity of tutte, jones, homfly and kauffman invariants (tutte polynomial, jones polynomial, homfly polynomial, kauffman polynomial)
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
Inequalities on the Number of Connected Spanning Subgraphs in a Multigraph
IEICE - Transactions on Information and Systems
On the Complexity of Matroid Isomorphism Problems
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Computation of chromatic polynomials using triangulations and clique trees
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
PReach: Reachability in Probabilistic Signaling Networks
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
| Hi-index | 0.00 |
We study the complexity of computing the coefficients of three classical polynomials, namely the chromatic, flow and reliability polynomials of a graph. Each of these is a specialization of the Tutte polynomial Σtijxiyj. It is shown that, unless NP = RP, many of the relevant coefficients do not even have good randomized approximation schemes. We consider the quasi-order induced by approximation reducibility and highlight the pivotal position of the coefficient t10 = t01, otherwise known as the beta invariant.Our nonapproximability results are obtained by showing that various decision problems based on the coefficients are NP-hard. A study of such predicates shows a significant difference between the case of graphs, where, by Robertson–Seymour theory, they are computable in polynomial time, and the case of matrices over finite fields, where they are shown to be NP-hard.