Results 1 - 10 of 218

Finding shortest non-separating and non-contractible cycles for topologically embedded graphs

by Sergio Cabello , Bojan Mohar - 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 ..."
Abstract - Cited by 46 (9 self) - Add to MetaCart
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

by T. J. Ford , 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 ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
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

by Robin Thomas, Xingxing Yu - 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. ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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

by Sergio Cabello - ACM Transactions on Algorithms
"... embedded graphs ∗ ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
embedded graphs ∗

Locally planar toroidal graphs are 5-colorable

by Michael O. Albertson, Walter, R. Stromquist - 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 ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
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

by Vivek S. Borkar, Vladimir Ejov, Jerzy A. Filar , 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 ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
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

by Sergio Cabello, Éric Colin de Verdière , Francis Lazarus , 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 ..."
Abstract - Cited by 8 (1 self) - Add to MetaCart
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

by Vivek S. Borkar, Vladimir Ejov, Jerzy A. Filar - 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 ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
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∗

by unknown authors , 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

by Colin Mcdiarmid - 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 ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
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