The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
Basic notions of universal algebra for language theory and graph grammars
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Graph operations and monadic second-order logic: a survey
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Parameterized Complexity
Lower bounds for treewidth of product graphs
Discrete Applied Mathematics
| Hi-index | 5.23 |
In this paper we describe an algorithm that, given a tree-decomposition of a graph G and a tree-decomposition of a graph H, provides a tree-decomposition of the cartesian product of G and H. Using this algorithm, we derive upper bounds on the treewidth (resp. on the pathwidth) of the cartesian product of two graphs, expressed in terms of the treewidth (resp. pathwidth) and the size of the factor graphs. In the context of graph grammars and graph logic, we prove that the cartesian product of a class of graphs by a finite set of graphs preserves the property of being a context-free set, and that the cartesian product by a finite set of connected graphs preserves MS"1-definability and MS"2-definability. We also prove that the cartesian product of two MS"2-definable classes of connected graphs is MS"2-definable.