Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The vertex separation number of a graph equals its path-width
Information Processing Letters
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
On the Clique-Width of Graphs in Hereditary Classes
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Context-free Handle-rewriting Hypergraph Grammars
Proceedings of the 4th International Workshop on Graph-Grammars and Their Application to Computer Science
On the Relationship between Clique-Width and Treewidth
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
On Approximation Hardness of the Bandwidth Problem
On Approximation Hardness of the Bandwidth Problem
On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree
SIAM Journal on Discrete Mathematics
New Graph Classes of Bounded Clique-Width
Theory of Computing Systems
On the relationship between NLC-width and linear NLC-width
Theoretical Computer Science
Clique-Width for 4-Vertex Forbidden Subgraphs
Theory of Computing Systems
Minimizing nLC-width is nP-complete
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
The relative clique-width of a graph
Journal of Combinatorial Theory Series B
Vertex-minor reductions can simulate edge contractions
Discrete Applied Mathematics
Polynomial algorithms for protein similarity search for restricted mRNA structures
Information Processing Letters
Graph parameters measuring neighbourhoods in graphs-Bounds and applications
Discrete Applied Mathematics
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph operations characterizing rank-width
Discrete Applied Mathematics
Recent developments on graphs of bounded clique-width
Discrete Applied Mathematics
A Complete Characterisation of the Linear Clique-Width of Path Powers
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
New Plain-Exponential Time Classes for Graph Homomorphism
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
On a disparity between relative cliquewidth and relative NLC-width
Discrete Applied Mathematics
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Finding branch-decompositions and rank-decompositions
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Graphs of linear clique-width at most 3
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
Maximal matching and path matching counting in polynomial time for graphs of bounded clique width
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Mike fellows: weaving the web of mathematics and adventure
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
| 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, that includes NP-hard problems) can be solved efficiently for graphs of small clique-width. It is widely believed that determining the clique-width of a graph is NP-hard; in spite of considerable efforts, no NP-hardness proof has been found so far. We give the first hardness proof. 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 NPhy complete. This solves a problem that has been open since the introduction of clique-width in the early 1990s.