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HDecompositions of rgraphs when H is an rgraph with exactly 2 edges
, 2010
"... Given two rgraphs G and H, an Hdecomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. The minimum number of parts in an Hdecomposition of G is denoted by φr H (G). By a 2edgedecomposition of an rgraph we mean an Hde ..."
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Given two rgraphs G and H, an Hdecomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. The minimum number of parts in an Hdecomposition of G is denoted by φr H (G). By a 2edgedecomposition of an rgraph we mean an Hdecomposition
Graphs and Combinatorics © SpringerVerlag 1986 Decomposition of the Complete rGraph into Complete rPartite rGraphs*
"... Abstract. For n> r> 1, let f,(n) denote the minimum number q, such that it is possible to partition all edges of the complete rgraph on n vertices into q complete rpartite rgraphs. Graham and Pollak showed that fz(n) = n 1. Here we observe that f3(n) = n 2 and show that for every fixed ..."
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Abstract. For n> r> 1, let f,(n) denote the minimum number q, such that it is possible to partition all edges of the complete rgraph on n vertices into q complete rpartite rgraphs. Graham and Pollak showed that fz(n) = n 1. Here we observe that f3(n) = n 2 and show that for every fixed
Minimum HDecompositions of Graphs
, 2006
"... Given graphs G and H, an Hdecomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let OEH (n) be the smallest number OE such that any graph G of order n admits an Hdecomposition with at most OE parts. Here we determine th ..."
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Cited by 7 (4 self)
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Given graphs G and H, an Hdecomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let OEH (n) be the smallest number OE such that any graph G of order n admits an Hdecomposition with at most OE parts. Here we determine
Rainbow matchings in rpartite rgraphs
"... Given a collection of matchings M = (M1,M2,...,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be srainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ: M → [q] suc ..."
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Cited by 2 (0 self)
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values of r,s and t and prove the conjecture when r = 2 or s = t = 2. In the case r = 3, a stronger conjecture is that in a 3partite 3graph if all vertex degrees in one side (say V1) are strictly larger than all vertex degrees in the other two sides, then there exists a matching of V1. This conjecture
Edge Detection
, 1985
"... For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the s ..."
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Cited by 1277 (1 self)
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about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
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