A distance approximating trees
نویسندگان
چکیده
منابع مشابه
Distance Approximating Trees: Complexity and Algorithms
Let Δ ≥ 1 and δ ≥ 0 be real numbers. A tree T = (V,E′) is a distance (Δ, δ)–approximating tree of a graph G = (V,E) if dH(u, v) ≤ Δ dG(u, v) + δ and dG(u, v) ≤ Δ dH(u, v) + δ hold for every u, v ∈ V . The distance (Δ, δ)-approximating tree problem asks for a given graph G to decide whether G has a distance (Δ, δ)-approximating tree. In this paper, we consider unweighted graphs and show that the...
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Let G = (V, E) be a connected graph endowed with the standard graph-metric dG and in which longest induced simple cycle has length λ(G). We prove that there exists a tree T = (V, F) such that |dG (u, v) − dT (u, v)| ≤ ⌊λ(G) 2 ⌋ + α for all vertices u, v ∈ V, where α = 1 if λ(G) = 4, 5 and α = 2 otherwise. The case λ(G) = 3 (i.e., G is a chordal graph) has been considered in Brandstädt, Chepoi, ...
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In this paper we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G2 of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus 2. Moreover, we prove that, if G is a strongly chordal graph or even a dually chordal graph, then there exists a spanning tree T of G that is an additive 3-spanner as wel...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.11.012