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Rankwidth and vertexminors
 J. COMBIN. THEORY SER. B
, 2005
"... The rankwidth is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Cliquewidth has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for treewidth. In this paper, we discuss the vertexminor relation of gr ..."
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Cited by 33 (7 self)
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of this paper is that for fixed k, there is a finite list of graphs such that a graph G has rankwidth at most k if and only if no graph in the list is isomorphic to a vertexminor of G. Furthermore, we prove that a graph has rankwidth at most 1 if and only if it is distancehereditary.
Graphs of bounded rankwidth
 Princeton University
, 2005
"... We define rankwidth of graphs to investigate cliquewidth. Rankwidth is a complexity measure of decomposing a graph in a kind of treestructure, called a rankdecomposition. We show that graphs have bounded rankwidth if and only if they have bounded cliquewidth. It is unknown how to recognize g ..."
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Cited by 22 (4 self)
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define graph vertexminors which generalizes matroid minors, and prove that if {G1, G2,...} is an infinite sequence of graphs of bounded rankwidth,
Vertexminors, Monadic Secondorder Logic, and a Conjecture by Seese
, 2006
"... We prove that one can express the vertexminor relation on finite undirected graphs by formulas of monadic secondorder 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 set ..."
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Cited by 17 (7 self)
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We prove that one can express the vertexminor relation on finite undirected graphs by formulas of monadic secondorder 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
GRAPHS OF SMALL RANKWIDTH ARE PIVOTMINORS OF GRAPHS OF SMALL TREEWIDTH
"... Abstract. We prove that every graph of rankwidth k is a pivotminor of a graph of treewidth at most 2k. We also prove that graphs of rankwidth at most 1, equivalently distancehereditary graphs, are exactly vertexminors of trees, and graphs of linear rankwidth at most 1 are precisely vertexmin ..."
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Cited by 3 (2 self)
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Abstract. We prove that every graph of rankwidth k is a pivotminor of a graph of treewidth at most 2k. We also prove that graphs of rankwidth at most 1, equivalently distancehereditary graphs, are exactly vertexminors of trees, and graphs of linear rankwidth at most 1 are precisely vertexminors
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
Unavoidable vertexminors in large prime graphs
 European J. Combin
"... Abstract. A graph is prime (with respect to the split decomposition) if its vertex set does not admit a partition pA,Bq (called a split) with A, B  ě 2 such that the set of edges joining A and B induces a complete bipartite graph. We prove that for each n, there exists N such that every prime g ..."
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Cited by 2 (2 self)
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graph on at least N vertices contains a vertexminor isomorphic to either a cycle of length n or a graph consisting of two disjoint cliques of size n joined by a matching. 1.
On kinetic waves: II) A theory of traffic Flow on long crowded roads
 Proc. Royal Society A229
, 1955
"... This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (? 2). From this a theory of the propagati ..."
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Cited by 489 (1 self)
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This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (? 2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (??2, 3). The theory is applied (?4) to the problem of estimating how a 'hump', or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a 'shock wave') on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (?5), and methods are obtained for estimating the extent and duration of the resulting holdup. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (? 6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject. 1.
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