## Deciding First-Order Properties of Locally Tree-Decomposable Graphs (1999)

Venue: | In Proc. 26th ICALP |

Citations: | 75 - 13 self |

### BibTeX

@INPROCEEDINGS{Frick99decidingfirst-order,

author = {Markus Frick and Martin Grohe},

title = {Deciding First-Order Properties of Locally Tree-Decomposable Graphs},

booktitle = {In Proc. 26th ICALP},

year = {1999},

pages = {105--135}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We introduce the concept of a class of graphs being locally tree-decomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded tree-width. We show that for each locally tree-decomposable class C of graphs and for each property ' of graphs that is denable in rst-order logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of tree-width of a graph. 3-Colorability, Hamiltonicity, and many other NP-complete properties of graphs can be decided in linear time when restricted to graphs whose tree-width is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a meta-theorem, which easily implies numer...