Uniform and minimal random spanning trees for finite graphs are well-known objects. Analogues of these for the nearest-neighbor graph on Z d have been studied by Pemantle and Alexander. Here we propose analogous definitions of uniform resp. minimal essential spanning forests for an infinite tree β«,
Minimal ratio spanning trees
β Scribed by R. Chandrasekaran
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 323 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0028-3045
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π SIMILAR VOLUMES
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in β«ήβ¬ d . Tightness of the distribution, as β¦ Βͺ 0, is establi
The N-cube is a graph with 2 N vertices and N 2 Ny1 edges. Suppose indepen- dent uniform random edge weights are assigned and let T be the spanning tree of minimal Ε½ . y 1 N Ο± y3 total weight. Then the weight of T is asymptotic to N 2 Γ i as N Βͺ Ο±. Asymp-is1 totics are also given for the local stru
## Abstract We show that if __G__ is a simple connected graph with and $|V(G)| \,\neq\,t+2$, then __G__ has a spanning tree withβ>β__t__ leaves, and this is best possible. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 37: 189β197, 2001
We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our Ε½ Ε½ .. Ε½ . algorithm r