eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-19
175
186
10.4230/LIPIcs.IPEC.2015.175
article
Definability Equals Recognizability for k-Outerplanar Graphs
Jaffke, Lars
Bodlaender, Hans L.
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. 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol043-ipec2015/LIPIcs.IPEC.2015.175/LIPIcs.IPEC.2015.175.pdf
treewidth
monadic second order logic of graphs
finite state tree automata
$k$-outerplanar graphs