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The monadic secondorder logic of graphs XVI: Canonical graph decompositions
 Logical Methods in Computer Science
, 2006
"... ..."
Circle graphs and Monadic Secondorder logic
, 2005
"... 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 representation as a set of intersecting chords, and we prove that this representation can be defined by monadic secondorder ..."
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Cited by 10 (4 self)
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formulas. By using the (canonical) split decomposition of a circle graph, one can define in monadic secondorder logic all its chord representations formalized as words with two occurrences of each letter. This construction uses the general result that the split decomposition of a graph can be constructed
The Expression Of Graph Properties And Graph Transformations In Monadic SecondOrder Logic
, 1997
"... By considering graphs as logical structures, one... ..."
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Cited by 160 (40 self)
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By considering graphs as logical structures, one...
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
The Monadic SecondOrder Logic Of Graphs XI: Hierarchical Decompositions Of Connected Graphs
, 1998
"... We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic SecondOrder Logic. This decomposition has two levels: every connected graph is a tree of "2connected components" called blocks ; every 2connected graph is a tree of socalled ..."
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Cited by 7 (6 self)
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We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic SecondOrder Logic. This decomposition has two levels: every connected graph is a tree of "2connected components" called blocks ; every 2connected graph is a tree of so
PrefixRecognisable Graphs and Monadic SecondOrder Logic
, 2001
"... We present several characterisations of the class of prefixrecognisable ..."
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Cited by 21 (2 self)
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We present several characterisations of the class of prefixrecognisable
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1300 (17 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
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