منابع مشابه
Degree Bounded Spanning Trees
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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* 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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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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We consider lower bounds on the number of spanning trees of connected graphs with degree bounded by d. The question is of interest because such bounds may improve the analysis of the improvement produced by memorisation in the runtime of exponential algorithms. The value of interest is the constant βd such that all connected graphs with degree bound ed by d have at least β d spanning trees wher...
متن کاملEmbedding nearly-spanning bounded degree trees
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion properties of G. As a result we show that for fixed d ≥ 2 and 0 < < 1, there exists a constant c = c(d, ) such that a random graph G(n, c/n) contains almost surely a copy of every tree T on (1− )n vertices with maximum degre...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2001
ISSN: 0178-4617,1432-0541
DOI: 10.1007/bf02679617