Languages that capture complexity classes
SIAM Journal on Computing
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
MFCS '89 Selected papers of the symposium on Mathematical foundations of computer science
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
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Connectivity and network flows
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 2)
Logical description of context-free graph languages
Journal of Computer and System Sciences
The closure of Monadic NP (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
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
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Extremal Graph Theory
Parameterized Complexity
Back and forth between guarded and modal logics
ACM Transactions on Computational Logic (TOCL)
Trees, grids, and MSO decidability: from graphs to matroids
Theoretical Computer Science - Parameterized and exact computation
The recognizability of sets of graphs is a robust property
Theoretical Computer Science
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
The Descriptive Complexity of Parity Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
On monadic second-order theories of multidominance structures
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
Universal structures and the logic of forbidden patterns
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
The modular decomposition of countable graphs: constructions in monadic second-order logic
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
| Hi-index | 5.23 |
We consider the class USk of uniformly k-sparse simple graphs, i.e., the class of finite or countable simple graphs, every finite subgraph of which has a number of edges bounded by k times the number of vertices. We prove that for each k, every monadic second-order formula (intended to express a graph property) that uses variables denoting sets of edges can be effectively translated into a monadic second-order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in USk. This result extends to the class of uniformly k-sparse simple hypergraphs of rank at most m (for any k and m).It follows that every subclass of USk consisting of finite graphs of bounded clique-width has bounded tree-width. Clique-width is a graph complexity measure similar to tree-width and relevant to the construction of polynomial algorithms for NP-complete problems on special classes of graphs.