Spanning trees with a bounded number of leaves
نویسندگان
چکیده
منابع مشابه
Spanning Trees with a Bounded Number of Leaves
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...
متن کاملSpanning trees with a bounded number of leaves in a claw-free graph
For a graph H and an integer k ≥ 2, let σk(H) denote the minimum degree sum of k independent vertices of H . We prove that if a connected claw-free graph G satisfies σk+1(G) ≥ |G| − k, then G has a spanning tree with at most k leaves. We also show that the bound |G| − k is sharp and discuss the maximum degree of the required spanning trees.
متن کاملApproximating 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...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2017
ISSN: 1232-9274
DOI: 10.7494/opmath.2017.37.4.501