A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings. The genus of a map is the minimal genus of an...
One of Courcelle’s celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO2) is fixed-parameter t...
A propositional system of modal logic is second-order if it contains quantifiers p and p, which, in the standard interpretation, are construed as ranging over sets of possible worl...
A circle graph is the intersection graph of a set of chords of a circle. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique rep...
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more ge...