The monadic second-order logic of graphs XV: On a conjecture by D. Seese

Vertex-minors, monadic second-order logic, and a conjecture by Seese

We prove that one can express the vertex-minor relation on finite undirected graphs by formulas of monadic second-order logic (with no edge set quantification) extended with a predicate expressing that a set has even cardinality. We obtain a slight weakening of a conjecture by Seese stating that sets of graphs having a decidable satisfiability problem for monadic second-order logic have bounded...

The Structure of Models of Decidable Monadic Theories of Graphs

Trees, grids, and MSO decidability: From graphs to matroids

Monadic second order (MSO) logic proved to be a useful tool in many areas of application, reaching from decidability and complexity to picture processing, correctness of programs and parallel processes. To characterize the structural borderline between decidability and undecidability is a classical research problem here. This problem is related to questions in computational complexity, especial...

Monadic Second Order Finite Satisfiability and Unbounded Tree-Width

The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese [24]. We prove that the following problem is decidable: Input: (i) A monadic second order logic sentence α, and (ii) a sentence β in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of α...

A Linear-time Recognition Algorithm for P4- a Unique Tree Representation for P4-sparse

7)) algorithm for the 3-clique-width problem. Preprint, 1998. Sha98] A. Sharell. Complexit e Descriptive et l'approximation des fonctions de d enombrement. J. Makowsky and U. Rotics. On the cliquewidth of graphs with few P4's. Linear time solvable optimization problems on certain structured graph families, extended abstract. Cou99] B. Courcelle. The monadic second order logic of graphs, XIV: un...