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218
Finding shortest non-separating and non-contractible 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 edge-lengths 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 (non-separating) facewidth of embedded graphs. Using similar ideas we provide the first nearlinear running time algorithm for computing the face-width 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 con-sists 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 quasi-compact 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 con-sists 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 quasi-compact noetherian locally ringed space which is not a
Five-Connected Toroidal Graphs Are Hamiltonian
- J. COMBIN. THEORY SER. B
, 1997
"... We prove that every edge in a 5-connected 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 5-connected 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 5-colorable
- 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 5-colored. 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 5-colored. 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 singu-larly perturbed (controlled) Markov chains. We also consider a func-tional 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 singu-larly perturbed (controlled) Markov chains. We also consider a func-tional 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 (con-trolled)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 (con-trolled)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
of
218