Reasoning in Argumentation Frameworks of Bounded Clique-Width
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Automata for monadic second-order model-checking
RP'11 Proceedings of the 5th international conference on Reachability problems
Exploiting restricted linear structure to cope with the hardness of clique-width
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
On the model-checking of monadic second-order formulas with edge set quantifications
Discrete Applied Mathematics
Characterising the linear clique-width of a class of graphs by forbidden induced subgraphs
Discrete Applied Mathematics
Tight complexity bounds for FPT subgraph problems parameterized by clique-width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Cluster vertex deletion: a parameterization between vertex cover and clique-width
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Cliquewidth and knowledge compilation
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in monadic second-order logic with second-order quantification on vertex sets, which includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph cannot be absolutely approximated in polynomial time unless $P = NP$. We also show that, given a graph $G$ and an integer $k$, deciding whether the clique-width of $G$ is at most $k$ is NP-complete. This solves a problem that has been open since the introduction of clique-width in the early 1990s.