Spanning trees with bounded degrees and leaves
نویسندگان
چکیده
منابع مشابه
Approximating bounded-degree spanning trees and connected factors with leaves
We present constant factor approximation algorithms for the following two problems: First, given a connected graph G = (V,E) with non-negative edge weights, find a minimum weight spanning tree that respects prescribed upper bounds on the vertex degrees. Second, given prescribed (exact) vertex degrees d = (di)i∈V , find a minimum weight connected d-factor. Constant factor approximation algorithm...
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For a spanning tree T of a graph G, we define the total excess te(T, k) of T from k as te(T, k) := ∑ v∈V (T )max{dT (v)− k, 0}, where dT (v) is the degree of a vertex v in T . In this paper, we show the following; if G is a 3-connected graph on a surface with Euler characteristic χ < 0, then G has a spanning ⌈8−2χ 3 ⌉ -tree T with te(T, 3) ≤ −2χ − 1. We also show an application of this theorem ...
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In 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph G with n ≥ 3 vertices, if d(u) + d(v) ≥ n − k + 1 for all non-adjacent vertices u and v of G (k ≥ 1), then G has a spanning tree with at most k leaves. In this paper, we generalize this result by using implicit degree sum condition of t (2 ≤ t ≤ k) independent vertices and we prove what follows: Let G be a connected graph...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.12.023