منابع مشابه
Percolation and Minimal Spanning Trees
Consider a random set V n of points in the box n; n) d , generated either by a Poisson process with density p or by a site percolation process with parameter p. We analyse the empirical distribution function F n of the lengths of edges in a minimal (Euclidean) spanning tree T n on V n. We express the limit of F n , as n ! 1, in terms of the free energies of a family of percolation processes der...
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Klimb, J., On the minimal covering of infinite sets, Discrete Applied Mathematics 45 (1993) 161-168. Minimal covering of infinite sets is studied. It is shown that if BC2’ is closed, then /* contains a minimal covering of X. If r// is a covering of X, then fl is closed on X if and only if there is an admissible functionf: X-1 4 which has no chain. For star type set systems Theorem 15 gives a su...
متن کاملFull Minimal Steiner Trees on Lattice Sets
Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it often proves far more tractable if we restrict our attention to points in special geometric configur...
متن کاملOn End-faithful Spanning Trees in Infinite Graphs
Let G be an infinite connected graph. A ray (from v) in G is a 1-way infinite path in G (with initial vertex v). An infinite connected subgraph of a ray R ⊂ G is called a tail of R. If X ⊂ G is finite, the infinite component of R\X will be called the tail of R in G\X. The following assertions are equivalent for rays P,Q ⊂ G: (i) There exists a ray R ⊂ G which meets each of P and Q infinitely of...
متن کاملOn spanning trees and k-connectedness in infinite graphs
If two rays P,Q ⊂ G satisfy (i)–(iii), we call them end-equivalent in G. An end of G is an equivalence class under this relation, and E(G) denotes the set of ends of G. For example, the 2-way infinite ladder has two ends, the infinite grid Z×Z and every infinite complete graph have one end, and the dyadic tree has 20 ends. This paper is concerned with the relationship between the ends of a conn...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2017
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-017-3380-x