منابع مشابه
Closure for Spanning Trees with k-Ended Stems
Let T be a tree. The set of leaves of T is denoted by ( ) Leaf T . The subtree ( ) Leaf T T − of T is called the stem of T . A stem is called a k-ended stem if it has at most k-leaves in it. In this paper, we prove the following theorem. Let G be a connected graph and 2 k ≥ be an integer. Let u and v be a pair of nonadjacent vertices in G . Suppose that ( ) ( ) 1 G G N u N v G k ≥ − − . Then ...
متن کاملClosure for spanning trees and distant area
A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with degG u + degG v ≥ n − 1, G has a spanning k-ended tree if and only if G + uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. W...
متن کاملSearching for Spanning k-Caterpillars and k-Trees
We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning kcaterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also, as a generalized versions of the depth-first search and the breadth-first search algorithms, we ...
متن کاملFinding the k Smallest Spanning Trees
We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log β(m,n) + k2); for planar graphs this bound can be improved to O(n+ k2). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k2n + n log n, k2 + kn log(n/k))). The k best orth...
متن کاملSpanning k-Trees of n-Connected Graphs
A tree is called a k-tree if the maximum degree is at most k. We prove the following theorem, by which a closure concept for spanning k-trees of n-connected graphs can be defined. Let k ≥ 2 and n ≥ 1 be integers, and let u and v be a pair of nonadjacent vertices of an n-connected graph G such that degG(u)+degG(v) ≥ |G|−1−(k−2)n, where |G| denotes the order of G. Then G has a spanning k-tree if ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2013
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-013-1314-z