منابع مشابه
Ends in Uniform Spanning Forests
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience. §
متن کاملMinimal spanning forests
We study minimal spanning forests in infinite graphs, which are weak limits of minimal spanning trees from finite subgraphs corresponding to i.i.d. random labels on the edges. These limits can be taken with free or wired boundary conditions, and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that ar...
متن کاملEnds in Uniform Spanning Forests 1
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.
متن کاملFinding Minimal Spanning Forests in a Grap
We propose two algorithms for solving a graph partitioning problem motivated by computational topology. Specifically, given a weighted, undirected graph G and a positive integer k, we desire to find k disjoint trees within G such that each vertex of G is contained in one of the trees and the weight of largest tree is as small as possible. We are unable to find this problem in the graph partitio...
متن کاملPercolation and Minimal Spanning Forests in Infinite Graphs
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2006
ISSN: 0091-1798
DOI: 10.1214/009117906000000025