Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
MSOL partitioning problems on graphs of bounded treewidth and clique-width
Theoretical Computer Science
On powers of graphs of bounded NLC-width (clique-width)
Discrete Applied Mathematics
Vertex-minor reductions can simulate edge contractions
Discrete Applied Mathematics
Polynomial algorithms for protein similarity search for restricted mRNA structures
Information Processing Letters
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The NLC-width and clique-width for powers of graphs of bounded tree-width
Discrete Applied Mathematics
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
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
H-join decomposable graphs and algorithms with runtime single exponential in rankwidth
Discrete Applied Mathematics
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
The clique-width of tree-power and leaf-power graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Rank-width and tree-width of H-minor-free graphs
European Journal of Combinatorics
Reasoning in Argumentation Frameworks of Bounded Clique-Width
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
On the Boolean-width of a graph: structure and applications
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
Graphs of separability at most two: structural characterizations and their consequences
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
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
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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
Graphs of separability at most 2
Discrete Applied Mathematics
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
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 unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
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
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
Hi-index | 0.03 |
Treewidth is generally regarded as one of the most useful parameterizations of a graph's construction. Clique-width is a similar parameterization that shares one of the powerful properties of treewidth, namely: if a graph is of bounded treewidth (or clique-width), then there is a polynomial time algorithm for any graph problem expressible in monadic second order logic, using quantifiers on vertices (in the case of clique-width you must assume a clique-width parse expression is given). In studying the relationship between treewidth and clique-width, Courcelle and Olariu [Discrete Appl. Math., 101 (2000), pp. 77--114] showed that any graph of bounded treewidth is also of bounded clique-width; in particular, for any graph G with treewidth k, the clique-width of G is at most 4 * 2k - 1 + 1.In this paper, we improve this result by showing that the clique-width of G is at most 3 * 2k - 1 and, more importantly, that there is an exponential lower bound on this relationship. In particular, for any k, there is a graph G with treewidth equal to k, where the clique-width of G is at least $2^{\lfloor k/2\rfloor - 1}$.