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The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs
  • B. Courcelle
  • Mathematics, Computer Science
  • Inf. Comput.
  • 1 March 1990
TLDR
We introduce the notion of a recognizable set of finite graphs, that is definable in monadic second-order logic. Expand
  • 1,298
  • 90
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Upper bounds to the clique width of graphs
TLDR
We bound the clique width of a graph in terms of its tree width on the one hand, and of its edge complement on the other, and investigate alternate hierarchical decompositions that apply to wider classes of graphs. Expand
  • 569
  • 68
  • PDF
Graph Rewriting: An Algebraic and Logic Approach
  • B. Courcelle
  • Computer Science, Mathematics
  • Handbook of Theoretical Computer Science, Volume…
  • 2 January 1991
TLDR
This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them and presents a comparison of the powers of several logical languages. Expand
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Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach
TLDR
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Expand
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Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width
TLDR
We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with ``too many'' induced paths with four vertices. Expand
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Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs ofExpand
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The Expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic
  • B. Courcelle
  • Mathematics, Computer Science
  • Handbook of Graph Grammars
  • 1 February 1997
  • 343
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Fundamental Properties of Infinite Trees
TLDR
A synthesis of various aspects of infinite trees, invcstigatcd bc diIlt*ic*nt ,tuthor\ III differenr contlbxts and hopes to he a unifying step towards a theor! of infinite trct.s. Expand
  • 298
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The Monadic Second-Order Logic of Graphs X: Linear Orderings
  • B. Courcelle
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 10 June 1996
Graphs are finite and handled as relational structures. We give some answers to the following general questions: 1. (1) For which classes of graphs C is it possible to specify a linear ordering ofExpand
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The Monadic Second-Order Logic of Graphs VIII: Orientations
  • B. Courcelle
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 31 March 1995
TLDR
Abstract In every undirected graph or, more generally, in every hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using quantifications on sets of edges or Hyperedges. Expand
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