منابع مشابه
A Property on Edge-disjoint Spanning Trees
The graphs in this note are finite and undirected . We allow multiple edges , but forbid loops . We shall use the notation of Bondy and Murty [1] , unless otherwise stated . Let G be a graph with E ( G ) ? [ . Let τ ( G ) denote the number of edge-disjoint spanning trees of G . For X ‘ E ( G ) , the notation G ( X ) denotes the spanning subgraph of G with edge set X , whereas G [ X ] denotes th...
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 کاملEdge-disjoint spanning trees and eigenvalues
Article history: Received 17 July 2013 Accepted 25 November 2013 Available online 13 December 2013 Submitted by R. Brualdi MSC: 05C50 15A18 15A42
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: European Journal of Combinatorics
سال: 1996
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0038