A Note on the Computability of Graph Minor ObstructionSets for Monadic Second Order
نویسندگان
چکیده
The major results of Robertson and Seymour on graph well-quasi-ordering establish nonconstructively that many natural graph properties that constitute ideals in the minor or immersion orders are characterized by a nite set of forbidden sub-structures termed the obstructions for the property. This raises the question of what general kinds of information about an ideal are suucient, or insuucient, to allow the obstruction set for the ideal to be eeectively computed. It has been previously shown that it is not possible to compute the obstruction set for an ideal from a description of a Turing machine that recognizes the ideal. This result is signiicantly strengthened in the case of the minor ordering. It is shown that the obstruction set for an ideal in the minor order cannot be computed from a description of the ideal in monadic second-order logic.
منابع مشابه
A Note on the Computability of Graph Minor Obstruction Sets for Monadic Second Order Ideals
The major results of Robertson and Seymour on graph well-quasi-ordering establish nonconstructively that many natural graph properties that constitute ideals in the minor or immersion orders are characterized by a nite set of forbidden substructures termed the obstructions for the property. This raises the question of what general kinds of information about an ideal are su cient, or insu cient,...
متن کاملGraph structure and Monadic second-order logic
Exclusion of minor, vertex-minor, induced subgraph Tree-structuring Monadic second-order logic : expression of properties, queries, optimization functions, number of configurations. Mainly useful for tree-structured graphs (Second-order logic useless) Tools to be presented Algebraic setting for tree-structuring of graphs Recognizability = finite congruence ≡ inductive computability ≡ finite det...
متن کاملTree-width and the monadic quantifier hierarchy
It is well known that on classes of graphs of bounded tree-width, every monadic second-order property is decidable in polynomial time. The converse is not true without further assumptions. It follows from the work of Robertson and Seymour, that if a class of graphs K has unbounded tree-width and is closed under minors, then K contains all planar graphs. But on planar graphs, three-colorability ...
متن کاملMonadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width. It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts. We first explain the role of Logic. A graph, eith...
متن کاملVertex-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...
متن کامل