منابع مشابه
The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues
We relate the tree-decompositions of hypergraphs introduced by Robertson and Seymour to the finite and infinité algebraic expressions introduced by Bauderon and Courcelle. We express minor inclusion in monadic second-order logic, and we obtain grammatical characterizations of certain sets of graphs defined by excluded minors. We show how tree-decompositions can be used to construct quadratic al...
متن کاملGraph equivalences and decompositions definable in Monadic Second-Order Logic. The case of Circle Graphs
Many graph properties and graph transformations can be formalized inMonadic Second-Order logic. This language is the extension of First-Order logic allowing variables denoting sets of elements. In the case of graphs, these elements can be vertices, and in some cases edges. Monadic second-order graph properties can be checked in linear time on the class of graphs of tree-width at most k for any ...
متن کاملThe monadic second-order logic of graphs XVI : Canonical graph decompositions
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 general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs hav...
متن کاملThe monadic second-order logic of graphs III: tree-decompositions, minor and complexity issues
We relate the tree-decompositions of hypergraphs introduced by Robertson and Seymour to the finite and infinité algebraic expressions introduced by Bauderon and Courcelle. We express minor inclusion in monadic second-order logic, and we obtain grammatical characterizations of certain sets of graphs defined by excluded minors. We show how tree-decompositions can be used to construct quadratic al...
متن کاملThe Monadic Second-Order Logic of Graphs XI: Hierarchical Decompositions of Connected Graphs
We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1989
ISSN: 0022-4049
DOI: 10.1016/0022-4049(89)90129-1