منابع مشابه
Decomposing the hypercube Qn into n isomorphic edge-disjoint trees
We show that the edge set of the n-dimensional hypercube Qn is the disjoint union of the edge sets of n isomorphic trees.
متن کاملEdge Disjoint Spanning Trees ∗
Let Zm be the cyclic group of order m ≥ 3. A graph G is Zm-connected if G has an orientation D such that for any mapping b : V (G) 7→ Zm with ∑ v∈V (G) b(v) = 0, there exists a mapping f : E(G) 7→ Zm − {0} satisfying ∑ e∈E+ D (v) f(e) − ∑ e∈E− D (v) f(e) = b(v) in Zm for any v ∈ V (G); and a graph G is strongly Zm-connected if, for any mapping θ : V (G) → Zm with ∑ v∈V (G) θ(v) = |E(G)| in Zm, ...
متن کاملEdge-connectivity and edge-disjoint spanning trees
where the minimum is taken over all subsets X of E(G) such that ω(G − X) − c > 0. In this paper, we establish a relationship 7 between λc(G) and τc−1(G), which gives a characterization of the edge-connectivity of a graph G in terms of the spanning tree 8 packing number of subgraphs of G. The digraph analogue is also obtained. The main results are applied to show that if a graph G is 9 s-hamilto...
متن کاملPartitioning the hypercube Q n into n isomorphic edge - disjoint trees
The problem of finding edge-disjoint trees in a hypercube e.g. arises in the context of parallel computing [3]. Independent of applications it is of high aesthetic appeal. A hypercube of dimension n, denoted by Qn, comprises 2 n vertices each corresponding to a distinct binary string of length n. An edge exists between two vertices if and only if their corresponding binary strings differ in exa...
متن کاملEdge-Disjoint Spanning Trees, Edge Connectivity, and Eigenvalues in Graphs
Let λ2(G) and τ (G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of τ (G), Cioabă and Wong conjectured that for any integers d , k ≥ 2 and a d -regular graph G, if λ2(G) < d − 2k−1 d+1 , then τ (G) ≥ k. They proved the conj...
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ژورنال
عنوان ژورنال: Journal of Computer Networks and Communications
سال: 2014
ISSN: 2090-7141,2090-715X
DOI: 10.1155/2014/498349