Ore’s condition for completely independent spanning trees
نویسندگان
چکیده
منابع مشابه
Two counterexamples on completely independent spanning trees
For each k ≥ 2, we construct a k-connected graph which does not contain two completely independent spanning trees. This disproves a conjecture of Hasunuma. Furthermore, we also give an example for a 3-connected maximal plane graph not containing two completely independent spanning trees.
متن کاملCompletely independent spanning trees in (partial) k-trees
Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that ⌈k/2⌉ ≤ cist(G) ≤ k − 1 for any k-tree G. Then...
متن کاملAlmost disjoint spanning trees: Relaxing the conditions for completely independent spanning trees
The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one ...
متن کاملA Note on the Degree Condition of Completely Independent Spanning Trees
Given a graph G, a set of spanning trees of G are completely independent if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. In this paper, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n−2, then there are at least n/3 completely independent spanning trees. Keyword: Completely independ...
متن کاملCompletely Independent Spanning Trees in Some Regular Graphs
Let k ≥ 2 be an integer and T1, . . . , Tk be spanning trees of a graph G. If for any pair of vertices (u, v) of V (G), the paths from u to v in each Ti, 1 ≤ i ≤ k, do not contain common edges and common vertices, except the vertices u and v, then T1, . . . , Tk are completely independent spanning trees in G. For 2k-regular graphs which are 2k-connected, such as the Cartesian product of a compl...
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: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.06.002