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The bidimensional theory of boundedgenus graphs
 SIAM JOURNAL ON DISCRETE MATHEMATICS
, 2004
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ON THE EXISTENCE OF INFINITELY MANY ESSENTIAL SURFACES OF BOUNDED GENUS
"... if M is an irreducible, ∂irreducible 3manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result in ..."
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Cited by 5 (0 self)
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if M is an irreducible, ∂irreducible 3manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result
Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus
 SIAM Journal of Discrete Mathematics
, 1996
"... This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any nvertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a set ..."
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Cited by 29 (4 self)
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This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any nvertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a
Fully dynamic algorithms for bounded genus graphs
, 1997
"... We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O(log n ..."
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We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O
Subexponential parameterized algorithms on graphs of boundedgenus and Hminorfree Graphs
"... ... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossing ..."
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Cited by 63 (22 self)
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... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, single
Compact Routing Tables for Graphs of Bounded Genus
, 2000
"... This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bitoperations per node to extract the route, for any constant > ..."
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Cited by 31 (12 self)
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; 0. We obtain the same bounds for graphs of crossingedge number bounded by o(n= log n), and we generalize for graphs of genus bounded by > 0 yielding a size of n log +O(n) bits per node. Actually we prove a sharp upper bound of 2n log k +O(n) for graphs of pagenumber k, and a lower bound of n log
Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs
, 2009
"... We present the first polynomialtime approximation schemes (PTASes) for the following subsetconnectivity problems in edgeweighted graphs of bounded genus: Steiner tree, lowconnectivity survivablenetwork design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orien ..."
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Cited by 18 (4 self)
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We present the first polynomialtime approximation schemes (PTASes) for the following subsetconnectivity problems in edgeweighted graphs of bounded genus: Steiner tree, lowconnectivity survivablenetwork design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both
Probabilistic embeddings of bounded genus graphs into planar graphs
 PROC. 23RD ANN. ACM SYMP. COMPUT. GEOM
, 2007
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Edge Separators For Graphs Of Bounded Genus With Applications
, 1993
"... We prove that every nvertex graph of genus g and maximal degree k has an edge separator of size O( gkn). The upper bound is best possible to within a constant factor. This extends known results on planar graphs and similar results about vertex separators. We apply the edge separator to the is ..."
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Cited by 8 (1 self)
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We prove that every nvertex graph of genus g and maximal degree k has an edge separator of size O( gkn). The upper bound is best possible to within a constant factor. This extends known results on planar graphs and similar results about vertex separators. We apply the edge separator
The Asymmetric Traveling Salesman Problem on Graphs with Bounded Genus
"... We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the HeldKarp linear programming relaxation has bounded orientable genus. 1 ..."
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We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the HeldKarp linear programming relaxation has bounded orientable genus. 1
Results 1  10
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981