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Constantdegree graph expansions that preserve treewidth
"... Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomialtime upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical conce ..."
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Cited by 2 (0 self)
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question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G = (V,E) admits an expansion G ′ = (V ′,E ′ ) with the maximum degree ≤ 3 and treewidth
Randomness conductors and the constantdegree expansions . . .
, 2001
"... The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: ¤¦¥¨§�©��� � , where � is the degree and © is an arbitrarily small constant. Such graphs are essential components in ..."
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Cited by 33 (2 self)
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The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: ¤¦¥¨§�©��� � , where � is the degree and © is an arbitrarily small constant. Such graphs are essential components
Domino treewidth
 DISCRETE MATH. THEOR. COMPUT. SCI
, 1994
"... We consider a special variant of treedecompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino treedecomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck;d such that ..."
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Cited by 87 (4 self)
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We consider a special variant of treedecompositions, called domino treedecompositions, and the related notion of domino treewidth. In a domino treedecomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant ck
Randomness Conductors and ConstantDegree LosslessExpanders
"... ABSTRACT The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 s^)D, where D is the degree and s ^ is an arbitrarily small constant. The best previous explicit constru ..."
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ABSTRACT The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 s^)D, where D is the degree and s ^ is an arbitrarily small constant. The best previous explicit
An Approximate MaxFlow MinCut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms
, 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf halfunits of commodity (uv) from u to v and f halfunits of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
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Cited by 246 (12 self)
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can prove that any nnode bounded degree graph, G, with minimum edge expansion h can be configured offline to simulate any nnode bounded degree graph H in 0(log n/a)steps using constant size queues. By letting H be a universal network, we can then use G to simulate a PRAM online with elay 0(log2 n1
Bandwidth, treewidth, separators, expansion, and universality
"... Abstract We prove that planar graphs with bounded maximum degree have sublinear bandwidth. As a consequence for each γ > 0 every nvertex graph with minimum degree ( 3 4 + γ)n contains a copy of every boundeddegree planar graph on n vertices. The proof relies on the fact that planar graphs have ..."
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have small separators. Indeed, we show more generally that for any class of boundeddegree graphs the concepts of sublinear bandwidth, sublinear treewidth, the absence of big expanders as subgraphs, and the existence of small separators are equivalent.
Bandwidth, treewidth, separators, expansion, and universality
"... We prove that planar graphs with bounded maximum degree have sublinear bandwidth. As a consequence for each γ> 0 every nvertex graph with minimum degree (3 4 + γ)n contains a copy of every boundeddegree planar graph on n vertices. The proof relies on the fact that planar graphs have small sepa ..."
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separators. Indeed, we show more generally that for any class of boundeddegree graphs the concepts of sublinear bandwidth, sublinear treewidth, the absence of big expanders as subgraphs, and the existence of small separators are equivalent.
Treewidth and Duality for Planar Hypergraphs.
"... We prove a conjecture of Robertson and Seymour (Graph Minors. III. Planar treewidth): the treewidth of a planar graph is at most the treewidth of its dual plus one. To this purpose, we study hypermaps, which represent hypergraphs on a surface. We dene a parallel composition on hypermaps which v ..."
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Cited by 11 (1 self)
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We prove a conjecture of Robertson and Seymour (Graph Minors. III. Planar treewidth): the treewidth of a planar graph is at most the treewidth of its dual plus one. To this purpose, we study hypermaps, which represent hypergraphs on a surface. We dene a parallel composition on hypermaps which
Treewidth and Small Separators for Graphs with Small Chordality
, 1995
"... A graph G kchordal, if it does not contain chordless cycles of length larger than k. The chordality cl of a graph G is the minimum k for which G is kchordal. The degeneracy or the width of a graph is the maximum mindegree of any of its subgraphs. Our results are the following: 1. The problem of ..."
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Cited by 3 (1 self)
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of treewidth remains NPcomplete when restricted on graphs with small maximum degree. 2. An upper bound is given for the treewidth of a graph as a function of its maximum degree and chordality. A consequence of this result is that when maximum degree and chordality are fixed constants, then there is a linear
Compact Navigation and Distance Oracles for Graphs with Small Treewidth
, 2011
"... Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build spaceefficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where the si ..."
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Cited by 3 (0 self)
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Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build spaceefficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where
Results 1  10
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283