Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
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
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Context-free Handle-rewriting Hypergraph Grammars
Proceedings of the 4th International Workshop on Graph-Grammars and Their Application to Computer Science
On the Clique-Width of Perfect Graph Classes
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
Compiling finite linear CSP into SAT
Constraints
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
SIAM Journal on Discrete Mathematics
Predicting learnt clauses quality in modern SAT solvers
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Clasp: a conflict-driven answer set solver
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Constrained-Path Labellings on Graphs of Bounded Clique-Width
Theory of Computing Systems
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
Characterising the linear clique-width of a class of graphs by forbidden induced subgraphs
Discrete Applied Mathematics
A combinatorial optimization algorithm for solving the branchwidth problem
Computational Optimization and Applications
Finding good decompositions for dynamic programming on dense graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Conflict anticipation in the search for graph automorphisms
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Survey: A survey of the algorithmic aspects of modular decomposition
Computer Science Review
Journal of Graph Theory
| Hi-index | 0.00 |
Clique-width is a graph invariant that has been widely studied in combinatorics and computer science. However, computing the clique-width of a graph is an intricate problem, the exact clique-width is not known even for very small graphs. We present a new method for computing the clique-width of graphs based on an encoding to propositional satisfiability (SAT) which is then evaluated by a SAT solver. Our encoding is based on a reformulation of clique-width in terms of partitions that utilizes an efficient encoding of cardinality constraints. Our SAT-based method is the first to discover the exact clique-width of various small graphs, including famous graphs from the literature as well as random graphs of various density. With our method we determined the smallest graphs that require a small pre-described clique-width.