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Isoperimetric Inequalities for Cartesian Products of Graphs
"... We give a characterization for isoperimetric invariants, including the Cheeger constant and the isoperimetric number of a graph. ..."
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Cited by 22 (0 self)
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We give a characterization for isoperimetric invariants, including the Cheeger constant and the isoperimetric number of a graph.
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning o ..."
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Cited by 374 (4 self)
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of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through a
EdgeIsoperimetric Problems for Cartesian Powers of Regular Graphs
 Theor. Comput. Sci
"... We consider an edgeisoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose cartesian powers the lexicographic order provides nested solutions for the EIP. We present several new classes of such graphs that include as special cas ..."
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Cited by 4 (0 self)
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cases all presently known graphs with this property. Our new results are applied to derive best possible edgeisoperimetric inequalities for the cartesian powers of arbitrary regular, resp. regular bipartite, graphs with a high density. 1 Introduction Let G = (V G ; EG ) be a graph and A; B VG
Isoperimetric Number of the Cartesian Product of Graphs and Paths
"... We prove that the isoperimetric number of Pk \Theta Gk , the Cartesian product of the path Pk and a connected graph with k vertices, is equal to the isoperimetric number of Pk itself. At the same time we construct an infinite family of graphs that shows that this is not true for Pk \Theta G where G ..."
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Cited by 4 (3 self)
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We prove that the isoperimetric number of Pk \Theta Gk , the Cartesian product of the path Pk and a connected graph with k vertices, is equal to the isoperimetric number of Pk itself. At the same time we construct an infinite family of graphs that shows that this is not true for Pk \Theta G where G
Fractional isoperimetric inequalities and subgroup distortion
 J. Amer. Math. Soc
, 1999
"... Abstract. It is shown that there exist infinitely many nonintegers r> 2 such that the Dehn function of some finitely presented group is ≃ n r. For each positive rational number s we construct pairs of finitely presented groups H ⊂ G such that the distortion of H in G is ≃ n s. And for each s ≥ 1 ..."
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Cited by 14 (1 self)
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s ≥ 1 we also construct finitely presented groups whose isodiametric function is ≃ n s. Introduction. For John Stallings, on his 60th birthday Isoperimetric inequalities measure the complexity of the word problem in finitely presented groups by giving a bound on the number of conjugates of relators
Isoperimetric Inequalities and the Width Parameters of Graphs?
"... Abstract. We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width of the ..."
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Abstract. We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width
An Isoperimetric Inequality for the Heisenberg Groups
"... . We show that the Heisenberg groups H 2n+1 of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ¸ L 2 ). This implies several important results about isoperimetric inequalit ..."
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Cited by 36 (0 self)
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. We show that the Heisenberg groups H 2n+1 of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ¸ L 2 ). This implies several important results about isoperimetric
Isoperimetric invariants for product markov chains and graph products
 COMBINATORICA
, 1996
"... Bounds on some isoperimetric constants of the Cartesian product of Markov chains are obtained in terms of related isoperimetric quantities of the individual chains. ..."
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Cited by 18 (3 self)
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Bounds on some isoperimetric constants of the Cartesian product of Markov chains are obtained in terms of related isoperimetric quantities of the individual chains.
Results 1  10
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158,548