منابع مشابه
Spanning trees with leaf distance at least four
For a graph G, we denote by i(G) the number of isolated vertices of G. We prove that for a connected graph G of order at least five, if i(G − S) < |S| for all ∅ = S ⊆ V (G), then G has a spanning tree T such that the distance in T between any two leaves of T is at least four. This result was conjectured by Kaneko in ”Spanning trees with constrains on the leaf degree”, Discrete Applied Math., 11...
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Given an undirected graph nding a spanning tree of the graph with maximum number of leaves is MAX SNP complete In this paper we give a new greedy approximation algorithm for maximum leaf spanning trees The running time O m n m n required by our algorithm where m is the number of edges and n is the number of nodes is almost linear in the size of the graph We also demonstrate that our analysis of...
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An independent set S of a connected graph G is called a frame if G − S is connected. If |S| = k, then S is called a k-frame. We prove the following theorem. Let k ≥ 2 be an integer, G be a connected graph with V (G) = {v1, v2, . . . , vn}, and degG(u) denote the degree of a vertex u. Suppose that for every 3-frame S = {va, vb, vc} such that 1 ≤ a < b < c ≤ n, degG(va) ≤ a, degG(vb) ≤ b − 1 and ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.09.027