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218
Finding shortest nonseparating and noncontractible cycles for topologically embedded graphs
 In Proceedings 13th European Symp. Algorithms
, 2005
"... Abstract. We present an algorithm for finding shortest surface nonseparating cycles in graphs with given edgelengths that are embedded on surfaces. The time complexity is O(g 3/2 V 3/2 log V + g 5/2 V 1/2 ), where V is the number of vertices in the graph and g is the genus of the sur This result ..."
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Cited by 46 (9 self)
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can be applied for computing the (nonseparating) facewidth of embedded graphs. Using similar ideas we provide the first nearlinear running time algorithm for computing the facewidth of a graph embedded on the projective plane, and an algorithm to find the facewidth of embedded toroidal graphs in O
The toroidal embedding arising from an irrational fan
, 1999
"... ABSTRACT. A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasicompact noetherian locally ringed space which is not a ..."
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Cited by 1 (1 self)
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ABSTRACT. A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasicompact noetherian locally ringed space which is not a
FiveConnected Toroidal Graphs Are Hamiltonian
 J. COMBIN. THEORY SER. B
, 1997
"... We prove that every edge in a 5connected graph embedded in the torus is contained in a Hamilton cycle. Our proof is constructive and implies a polynomial time algorithm for finding a Hamilton cycle. ..."
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Cited by 2 (0 self)
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We prove that every edge in a 5connected graph embedded in the torus is contained in a Hamilton cycle. Our proof is constructive and implies a polynomial time algorithm for finding a Hamilton cycle.
Finding shortest contractible and shortest separating cycles in embedded graphs
 ACM Transactions on Algorithms
"... embedded graphs ∗ ..."
Locally planar toroidal graphs are 5colorable
 Proc. Amer. Math. Soc
, 1982
"... Abstract. If a graph can be embedded in a torus in such a way that all noncontractible cycles have length at least 8, then its vertices may be 5colored. The conclusion remains true when some noncontractible cycles have length less than 8, if the exceptions are all homotopic. Essentially this hypoth ..."
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Cited by 7 (2 self)
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Abstract. If a graph can be embedded in a torus in such a way that all noncontractible cycles have length at least 8, then its vertices may be 5colored. The conclusion remains true when some noncontractible cycles have length less than 8, if the exceptions are all homotopic. Essentially
On the Hamiltonicity gap and doubly stochastic matrices
, 2006
"... We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)entry of the fundamental matrices of the Markov chains induced by these policies. We fo ..."
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Cited by 1 (1 self)
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We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)entry of the fundamental matrices of the Markov chains induced by these policies. We
Finding cycles with topological properties in embedded graphs
, 2010
"... Let G be a graph cellularly embedded on a surface. We consider the problem of determining whether G contains a cycle (i.e. a closed walk without repeated vertices) of a certain topological type. We show that the problem can be answered in linear time when the topological type is one of the following ..."
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Cited by 8 (1 self)
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Let G be a graph cellularly embedded on a surface. We consider the problem of determining whether G contains a cycle (i.e. a closed walk without repeated vertices) of a certain topological type. We show that the problem can be answered in linear time when the topological type is one
Directed graphs, Hamiltonicity and doubly stochastic matrices
 RANDOM STRUCTURES AND ALGORITHMS
, 2004
"... We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled)Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)entry of the fundamental matrices of the Markov chains induced by the same policies. In p ..."
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Cited by 2 (1 self)
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We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled)Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)entry of the fundamental matrices of the Markov chains induced by the same policies
Finding cycles with topological properties in embedded graphs∗
, 2010
"... Let G be a graph cellularly embedded on a surface. We consider the problem of determining whether G contains a cycle (i.e. a closed walk without repeated vertices) of a certain topological type. We show that the problem can be answered in linear time when the topological type is one of the following ..."
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Let G be a graph cellularly embedded on a surface. We consider the problem of determining whether G contains a cycle (i.e. a closed walk without repeated vertices) of a certain topological type. We show that the problem can be answered in linear time when the topological type is one
A doubly cyclic channel assignment problem
 Discrete Applied Mathematics
, 1997
"... A standard model for radio channel assignment involves a set V of sites, the set (0, 1,2,..} of channels, and a constraint matrix (w(u,v)) specifying minimum channel separations. An assignment f: V + {0,1,2,...} is feasible if the distance I.f(u) f(u)1 b w(u, u) for each pair of sites u and u. The ..."
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Cited by 2 (1 self)
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A standard model for radio channel assignment involves a set V of sites, the set (0, 1,2,..} of channels, and a constraint matrix (w(u,v)) specifying minimum channel separations. An assignment f: V + {0,1,2,...} is feasible if the distance I.f(u) f(u)1 b w(u, u) for each pair of sites u and u
Results 1  10
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218