منابع مشابه
Degree-bounded minimum spanning trees
* to be exact, times the weight of a minimum spanning tree (MST). In particular, we present an improved analysis of Chan’s degree-4 MST algorithm [4]. Previous results. Arora [1] and Mitchell [9] presented PTASs for TSP in Euclidean metric, for fixed dimensions. Unfortunately, neither algorithm extends to find degree-3 or degree-4 trees. Recently, Arora and Chang [3] have devised a quasi-polyno...
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We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical degree-bounded MST problem, where for every vertex v, a simple upper bound on the degree is imposed. Iterative rounding/relaxation algorithms became the tool of choice for ...
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In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set S ⊆ V(G) of cardinality n(k − 1) + c + 2, there exists a vertex set X ⊆ S of cardinality k such that the degree sum of vertices in X is at least |V(G)| − c − 1. Then G has a spanning tree T with maximum de...
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a r t i c l e i n f o a b s t r a c t In this paper, we study the problem of computing a spanning tree of a given undirected disk graph such that the radius of the tree is minimized subject to a given degree constraint *. We first introduce an (8, 4)-bicriteria approximation algorithm for unit disk graphs (which is a special case of disk graphs) that computes a spanning tree such that the degre...
متن کاملSpanning Trees of Bounded Degree
Dirac’s classic theorem asserts that if G is a graph on n vertices, and δ(G) ≥ n/2, then G has a hamilton cycle. As is well known, the proof also shows that if deg(x) + deg(y) ≥ (n− 1), for every pair x, y of independent vertices in G, then G has a hamilton path. More generally, S. Win has shown that if k ≥ 2, G is connected and ∑ x∈I deg(x) ≥ n− 1 whenever I is a k-element independent set, the...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2008.03.037