One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known as Courcelle’s Theorem [6]. These algorithms are constructed as finite state tree automata, and hence every CMSOL-definable graph property is recognizable. Courcelle also conjectured that the converse holds, i.e. every recognizable graph property is definable in CMSOL for graphs of bounded treewidth. We prove this conjecture for k-outerplanar graphs, which are known to have treewidth at most 3k − 1 [2].
treewidth, monadic second order logic of graphs, finite state tree automata, k-outerplanar graphs
Models of Computation (acm F.1.1)
Null option (theme 11)
International Symposium on Parameterized and Exact Computation
This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/024.002.003 - Networks
Algorithms and Complexity

Jaffke, L, & Bodlaender, H.L. (2015). Definability Equals Recognizability for k-Outerplanar Graphs. In Proceedings of International Symposium on Parameterized and Exact Computation 2015 (IPEC 10) (pp. 175–186). doi:10.4230/LIPIcs.IPEC.2015.175